When I went through API my son had just turned 1. It's not as bad as people make it out to be. I had an office at home and was always in there studying and a couple of times an hour my son would woddle over and want to play. It was a welcome break from studying, and they recommend that you study for 20-30 min, then take a 3-4 minute break, so that worked out nicely. The wife knew what I had to do and was very understanding. We didn't have much family time during the week for the first 4 weeks of API. I'd take one day, usually Sat and spend it with the Fam.
Everyone talks about how hard it would be to get through flight school being married, and even more so with children. I just finished Primary and haven't had a problem studying, or spending time with family. It's been a blast!