Transferring to a UC is more difficult from a CSU than it is from a Community College. UC’s (by policy) open more opportunities for CC students, on the theory that CC is a 2-year degree. CSU is presumed to be your choice, not a pathway to UC, and offers a 4-year education, so by policy, UC figures that Community College students should be given preference in transferring.
Please ask at the transfer center of your target UC before you start classes anywhere, as you would hate for a policy position to affect your life choices. You may find out that your best solution for family as well as university options is to complete your first 2 years at a local community college.