If the Hotel New York gives you 8am entry to the apart, use it! Peter Pan's Flight, Dumbo, Carousel (in Fantasyland) and Buzz Laser Blast and Orbitron rides all open at 8am and when we went (recently) the queues before 9am were minimal. With a bit of luck you can ride all of them, some twice, by 10am.
Dumbo and Peter Pan, and Buzz, have the biggest queues.
At 10am the Park opens to all. Head to Alice's Labyrinth first, then the Conte de Fees boat ride and Casey's Circus Train behind it. These should still all be quiet for the next hour or so. And It's a Small World - the queues move quickly.
By 11-ish start thinking about lunch, get in early.
There is a "Coin bebe" (baby centre) in the centre of the park and that is the ONLY place you can warm up bottles and food, in the microwaves, and they have high chairs for feeding if needed. Baby facilities elsewhere are patchy.
Rent a stroller at the entrance, even if your DC1 is a good walker. You'll get to the other end of the park MUCH faster that way. They are also great ways to stake out your pitch for the 7pm parade. Stake your pitch for this about an hour before using the buggies, then take it in turns to take the DCs off to do things whilst the other guards the pitch. Be careful where you stand, the sun could be in your eyes (outside the cars store). At the very end of the parade is a good quiet place and you can escape easily if you want to leave the park straight after.
Agree the Brit Guide is fab.
As for Studios, the Slinky Dog ride is about all they can do in the Toy Story area (no 8am entry here). There is the flying carpet ride but queues are big. The Playhouse Disney show is good - was at 12.15pm when we went (in English, 11.15am show was French the day we went) but you need to arrive earlier for a place.
Studios also only had one baby room with microwave. Oh, and you can't take pushchairs in the baby rooms. 
You can buy baby food in the Park and Studios but they only have two varieties. Take your own food, but buy the kind in a bowl not pouches, as they don't supply bowls or anything like that.
They do supply some paper bibs and some high chairs. But these were hit-and-miss.
What else? Rainforest Cafe in the Village is good for kids and a walk by the lake, where your hotel is anyway, and you can hire pedalos and little boats there too.
Mickey/Minnie ears are obligatory 