UPDATED:

[I deleted most of my original comment. Additional information is now available that makes my original theory untenable.]

Juana Gómez, Joachin Gómez, Ynes Gómez and Gaspar Gómez are all listed in the 1669 Padrón de Santa María de los Lagos as part of the household of Antonio de Aguirre and his wife, Isabel Gómez AKA Ortiz (daughter of Pedro Gómez de Portugal and Isabel Ortiz de Anda):

estancia o casa de Antonio deaguirre
Ysavel Gomez Sumuger - ++
Juana gomez Soltera - ++
Pedro martin casado con - ++
Ynes gomez - ++
Joachin gomez - ++
gaspar gomez - ++
Magdalena Gutierres sumuger - ++

https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KTXV

My family is descended from three of the four (Juana, Gaspar and Joachin), so the question of their identity is important to us. 

I originally proposed some or all of them were Isabel's children by a previous relationship. I was wrong. Newly discovered information now verifies the relationships between Juana, Joachin and Gaspar Gómez, as well as sets the estimated dates of birth for Juana and Gaspar back considerably to be more in line with the date of birth of Isabel Gómez AKA Ortiz. She cannot be their mother, but may instead be their sister. 

A 1709 Dispensa Matrimonial establishes:

  • Juana Gómez and Gaspar Gómez are hermanos.
  • Joachin Gómez is Juana's son and Gaspar's nephew.
  • Gaspar Gómez is married to Magdalena de Ayala AKA Gutiérrez AKA del Vargas (as seen in the 1669 padrón), and they share a son named Antonio.
  • Maria Gómez is daughter of Joachin Gómez and Juana de Ysassi, and is granddaughter of Juana Gomez. She and her cousin, Antonio Gómez, are engaged to be married.

https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSXG-6SW6-7

While I'm certain Ynes Gómez AKA Hortis (from the de Aguirre household in the 1669 padron) is related to this group, the nature of this relationship isn't yet determined.

____________

Below are transcriptions from the 1676 Padron de Lagos concerning the Aguirre and allied households and afterwards a tree with all sources cited.

Transcription of the household of Antonio de Aguirre and Isabel Gómez AKA Ortiz, from image 49 of the 1676 Padron de Santa Maria de los Lagos:

Rancho de Ant.o deaguirre
Ant.o deAguirre Esp C++
Ysabel Ortiz ++
Joseph de aguirre S++
Ant.o Ortiz s++
Ju.o de aguirre Esp de 11años

https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KYM7

From image 30 of the 1676 Padron de Santa María de los Lagos:

Cassa de Joseph Sanches
Joseph Sanches Esp C++ [husband of Aldonza Ortiz of about 4 years at this time]
Aldonza ortiz de Aguirre Esp++ [Aldonza uses both parents' surnames despite being born almost 10 years before their marriage in 1666] 
Nicolas de Aguirre niño de 9 años [son of Antonio de Aguirre and Isabel Gómez AKA Ortiz, younger brother of Aldonza]
Pasqual Delacruz Y C++ [Servant?]
thereza Ma Y ++ [Servant?]

https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KYNC

From image 31 of the 1676 Padron de Santa María de los Lagos:

Cassa de Cat.n de Ortega
Cat.n de Ortega Esp V++  [Catalina de Ortega, viuda de Bartolome Martín]
Nicolas martín Esp s++ [son of Catalina de Ortega and Bartolome Martín]
P.o martín C++ Ynes gomes ++ [Pedro Martín, son of Catalina de Ortega and Bartolome Martín. Husband of Ynes Gómez]
Ysabel martin Esp s++ [daughter of Pedro Martín and Ynés Gómez, namesake of Isabel Gómez AKA Ortiz or Isabel Ortiz de Anda?]

https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KY6R

_______________

Below is a tree based upon the latest information:

***Unproven children in italics***

1st Generation of the proposed household of Antonio de Aguirre as seen in the 1669 and 1676 padrons:

  • Siblings Isabel Gómez AKA Ortiz, Juana Gómez AKA de Anda and Gaspar Gómez:

1.1 Isabel Gómez AKA Ortiz
1st cc?
2nd cc 1666 Antonio de Aguirre (Español)
https://www.familysearch.org/ark:/61903/3:1:9392-G5YL-F

1.2 Juana Gómez AKA Juana de Anda (Española)
cc ????
1709 Dispensa Matrimonial (sister to Gaspar Gómez and mother of Joachin Gómez): https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSXG-6SW6-7
1635 (Madrina as Juana de Anda with her brother Gaspar Gómez as padrino): https://www.familysearch.org/ark:/61903/3:1:9392-G5TH-J
1663 (Madrina with her father Pedro Gómez de Portugal as padrino): https://www.familysearch.org/ark:/61903/3:1:9392-G5TV-1

1.3 Gaspar Gómez (Español, mestizo)
d. 1684
cc 11 Apr 1649 Ana de Quesada
Marriage to 1st wife: https://www.familysearch.org/ark:/61903/3:1:9392-G5BF-W ("fueron testigos Joseph Gomez Portugal padrinos. y Joana Masias")
cc (prob c1666-c1668) doña Magdalena Gutiérrez AKA de Ayala AKA del Vargas (Española)
1669 Padron de Lagos: https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KTXV
1709 Dispensa Matrimonial (brother to Juana Gómez; uncle of her son, Joachin Gómez; husband of Magdalena de Ayala and father of Antonio Gómez): https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSXG-6SW6-7
(Padrino with sister "Juana de Anda" as madrina): https://www.familysearch.org/ark:/61903/3:1:9392-G5TH-J
(1684 burial of Gaspar Gómez, husband of dona Magdalena del Vargas): https://www.familysearch.org/ark:/61903/3:1:9392-VY9X-G8
(1721 burial of "Magdalena de Allala, espanola viuda ... de Gaspar Gomez"): https://www.familysearch.org/ark:/61903/3:1:9392-K39V-MF

2nd Generation of the proposed household of Antonio de Aguirre as seen in the 1669 and 1676 padrons:

  • Children born to Isabel Ortiz prior to her 1666 marriage with Antonio de Aguirre:

1.1.1 Aldonsa Ortiz AKA de Aguirre (mestiza, Española) 
cc 1672 José Sánchez (mestizo, Español)
https://www.familysearch.org/ark:/61903/3:1:9392-G5Y1-W
https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KYNC

1.1.2 Antonio de Ortiz?
https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KYM7

  • Known children born to Isabel Gómez AKA Ortiz after her 1666 marriage with Antonio de Aguirre:

1.1.3 Juan de Aguirre (Español)
n. c1666
https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KYM7

1.1.4 Nicolas de Aguirre (mestizo)
n. c1667
https://www.familysearch.org/ark:/61903/3:1:33SQ-GG2J-748
https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KYNC

  • Child of Juana Gómez AKA de Anda:

1.2.1 Joachin Gómez (mestizo)
cc Juana de Ysassi (morisca, mestiza) (Sister of Maria de Ysassi and Ygnacio de Ysassi below)
1669 Padron: https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KTXV
1678 Marriage to Juana de Ysassi: https://www.familysearch.org/ark:/61903/3:1:9392-VY9J-FX
Dispensa matrimonial de Juan Javier Isassi y su bisnieta María Guadalupe Gómez (1780): https://www.familysearch.org/ark:/61903/3:1:9392-6L9C-PP (Lists Joachin and Gertrudis Gómez as siblings. They should be primos hermanos, or 1st cousins. I believe this dispensa erroneously left out their parents' generation: siblings Juana Gómez AKA de Anda and Gaspar Gómez)  
1709 Dispensa Matrimonial (son of Juana Gómez, nephew of Gaspar Gómez, husband of Juana de Ysassi, father of Maria Gómez and cousin of Antonio Gómez): https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSXG-6SW6-7

  • Children of Gaspar Gomez and Ana de Quesada:

1.3.1 Pedro Gómez
n. 1649, b. 14 Nov 1649 padrinos: Pedro Gomez Portugal & Ysabel Ortis
https://www.familysearch.org/ark:/61903/3:1:9392-G5BR-X

1.3.2 Nicolás Gómez de Portugal AKA Maravilla (mestizo, Español)
cc 14 Nov 1674 María de Ysassi AKA Díaz (sister of Juana de Ysassi above and Ygnacio de Ysassi below)
"hijo legitimo de Gaspar Gomes de Portugal i Ana de Quesada defuncta" and Padrinos: Ygnacio Gutiérrez y doña Juana Rincon, sumuger (related to Gaspar's second wife, Magdalena Gutierrez AKA de Ayala AKA del Vargas?).
Listed with wife's family in 1676 padron of Lagos: https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KR24
d. 1688: https://familysearch.org/ark:/61903/3:1:9392-VY9X-61

  • Children of Gaspar Gómez and doña Magdalena Gutiérrez AKA de Ayala AKA del Vargas:

1.3.3 Joseph Gómez (Español)
cc 1688 Ana de Avalos (mestiza), daughter of Francisco de Abalos & Francisca de Retamossa
https://www.familysearch.org/ark:/61903/3:1:9392-VY9N-L7

1.3.4 Agueda Gómez (Española)
cc 1693 Gabriel Ortiz (Español), son of Gabriel Ortiz de Anda (Español, mestizo) & Josepha de Ortega (mestiza)
1639 Baptism of the elder Gabriel Ortiz (son of Pedro Ortiz de Anda and Ana Ramírez): https://www.familysearch.org/ark:/61903/3:1:9392-G5RJ-H
1693 Marriage: https://www.familysearch.org/ark:/61903/3:1:9392-VY9F-8Y

1.3.5 Gertrudis Gómez
cc Ygnacio de Ysassi (brother of María de Ysassi AKA Díaz and Juana de Ysassi above)
Ygnacio in the 1676 Padron: https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KR24
Dispensa matrimonial de Juan Javier Isassi y su bisnieta María Guadalupe Gómez (1780): https://www.familysearch.org/ark:/61903/3:1:9392-6L9C-PP (Lists Joachin and Gertrudis Gómez as siblings. They should be primos hermanos, or 1st cousins. I believe this dispensa erroneously left out their parents' generation: siblings Juana Gómez AKA de Anda and Gaspar Gómez)
Dispensa matrimonial de su bisnieto José Mariano de Isassi y María Francisca Gómez (1798):
https://www.familysearch.org/ark:/61903/3:1:9392-65RH-9

1.3.6 Antonio Gómez (mestizo)
n. 1683
cc 1709 María Gómez (mestizo), daughter of Joachin Gómez above and 1st cousin once removed from her husband, see  
https://www.familysearch.org/ark:/61903/3:1:9392-K9F7-9
1709 Dispensa Matrimonial: https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSXG-6SW6-7
Dispensa matrimonial de su bisnieto José Mariano de Isassi y María Francisca Gómez (1798):
https://www.familysearch.org/ark:/61903/3:1:9392-65RH-9

3rd Generation of the proposed household of Antonio de Aguirre as seen in the 1669 and 1676 padrons:

1.2.1.1 María Gómez (mestizo), daughter of Joachin Gómez above and 1st cousin once removed from her husband.
cc Antonio Gómez n. 1683, son of Gaspar Gómez and Magdalena Gutierrez AKA de Ayala AKA del Vargas
1709 Dispensa Matrimonial: https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSXG-6SW6-7

__________

Listed in the 1669 padron as part of Antonio de Aguirre's household, but unsured how she fits into the family:

Ynes Gómez AKA Hortiz (Española)
cc 1663 Pedro Martin (Español)
https://www.familysearch.org/ark:/61903/3:1:9392-G5RT-K
https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KTXV
https://www.familysearch.org/ark:/61903/3:1:3QS7-L9K8-KY6R