Solá, a Basque, was the last Spanish governor of Alta California, serving from 1815–1822 at the Presidio of Monterey. Did he have a wife and family, there or elsewhere?
In California Through Russian Eyes, 1806–1848, on page 158, there is a discussion of a celebration being held in honor of the Tsar's birthday. Entertainment in the form of dancing and singing caused mention of two young girls 'sweet voices'. One of the girls who 'distinguished herself' is listed as Dona Josefa de Sola. The footnote credits her as 'The daughter of Governor Pablo Vincente de Sola'.
That is the only indication of family (besides his brother) that I find. Since he died in Mexico City in 1826, perhaps records might be found there, such as a will or burial site near other kin.
According the site Leinztarra, Solá was married to Nicolasa Sufriategui Arangoitia, with whom he had a son, Antonio Vicente Solá Sufriategui, born 1778.
Donald Nuttall's 1972 paper "The Gobernantes of Spanish Upper California: A Profile", concludes that he was not, but perhaps failed to uncover this detail.