According to what I have been able to investigate, the children of Francisco Suárez de Ibarra (ca.1577-1641), Alférez Real de Guadalajara, were the following:

From his marriage to María Martínez del Castillo (died in 1622):
Juana de Ibarra y Martínez del Castillo (b. 1603-, married to Antonio Villar de las Casas
Mariana de Ibarra y Martínez del Castillo (ca.1605-1630, married to Gerónimo Velázques y Dávila
Francisco de Ibarra y Martínez del Castillo (ca 1607-?), a Jesuit
Francisco de Ibarra y Martínez del Castillo (ca 1610-?), married to Beatriz Gutiérrez de Carriazo, he moved to Mexico City and his children were born there.
(I really don't know which of the two Franciscos was born first)

From his marriage to Isabel Pimentel and Hurtado (1603-1665)
Francisco de Ibarra y Pimentel (ca 1625- before 1698), married to Elena de Vargas
Alonso de Ibarra y Pimentel (ca 1626-?), Franciscan friar; professed April 6, 1647, at the San Francisco Convent in Guadalajara.
Miguel de Ibarra y Pimentel (1631-?), married to Agustina Zúñiga y Vizcaíno (great-granddaughter of the navigator Sebastián Vizcaino, explorer of the California coast)
María de Ibarra y Pimentel (1635-?)
Joseph de Ibarra y Pimentel (1636-?)
Juan de Ibarra y Pimentel (1640-1718), married to Teresa de Sabalsa, settled in Tepic, becoming a prosperous merchant.

I have the strong theory, due to several coincidences in dates and godparents, that Miguel de Ibarra and Agustina de Zúñiga and Vizcaíno were the parents of my direct ancestor Francisco de Ibarra, married to Lorenza de la Plaza and settled in Ixtlán del Río , Nayarit, who died in 1739.