This may not help at this point, but in normal circumstances, the babysitter will stay until a parent returns home. Also, you can call a babysitter even when you aren't going out. The babysitter will come and help with the babies while mom and dad take care of other things around the house. In this case, the babysitter stays until midnight.
I think a babysitter will have to come when the triplets go to school. The game won't let a baby be home alone.