Well,
At IOA there is a restaurant called Confisco Grille and Bar. It's located to the right as you walk into Port of Entry, just before Seuss Landing. Meaning, you enter the park, go down the entry way, then you can go left (hulk) or right (Suess). Go right and the restaurant is on the right next to some bathrooms.
Go there during lunch and the characters walk around and you can take pictures with them. They serve beer at the bar, so if you have a husband, or a partner, then you can have a few drinks while the other person watches the kids in the Seuss playground and the kiddie rides. The kids love the playground area, they will stay in there for an hour.
I don't understand why people would want to spend breakfast with characters and make it a big thing.
The early morning hours are the best time to get on all the rides before the crowd hits. If you goto breakfast with characters, and spend 2 hours doing it, then your morning is gone and you face long lines in the afternoon.
Yes, you can visit both parks in two days, if you get there early in the morning and go on the rides first. IOA gets busy in the afternoon, the morning and hour before close are good. On Wednesday, IOA opens at 8am for people with multi-day tickets, otherwise it's 9am. Be at the gate half an hour before it opens. Do all the rides then goto Confisco's for lunch at 11am before the crowd hits that place. If your kids can handle the walk, then hop over to US and visit that park in the afternoon. MIB will have an hour wait, but you can get on the other rides and the kids can go to the climbing area and the water play area if you want. Then it's back to IOA before they close.
The key is to be at the park gate before it opens.