We are renting a car through Costco. I've read parking is fine early but difficult as the morning goes on. That, plus traffic, are my reasons for getting an early start.
Note that there is a 4 hour minimum for the sitter, so you would be paying for that time either way. We elected to do the sitter all day rather than have her drop them at Aunty's but I think you could do either one. But, I think if the kids are at Aunty's for lunch and/or dinner, you have to wait in line the day-of to get them on the meal list (even though they may be registered for a free activity that day, meals are not included unless it is a premium (paid) activity). I don't think you can sign up for the meals until Aunty's "opens" at 8am, so that blows up the plan of you leaving early for PH. One option would be to pre-register them for the preimium Fish are Friends, if offered on your PH day, as that includes lunch. Then babysitter 0630-1030, sitter drops at Aunty's, you pick them up before dinner. So no standing in line that morning.