*cracks knuckles* Well, we've done a LOT of travel with our gaggle of kids, including several Disney trips. Here are some things to consider:
On the way: each kid has a backpack with a favorite blanket and stuffed animal. Empty water bottle, too. Make sure to have a change of clothes for each kid in your carry-on just in case, and I suggest a couple of gallon-size ziplok bags as well, in case they throw up or have a potty accident. Diaper wipes are great for cleaning up most messes, too. Bring familiar snacks, and plenty of activities. It's a long flight from NY to LA.
At Disney: I despise what Disney has done with Genie+ and lightning lanes, but I suppose they kind of have to in order to balance supply and demand. There are two Disney parks, and you can either get single-park tickets (you only get in to one park per day) or park hopper tickets (so you can go from park to park). The parks are big enough that you don't need the extra expense of the Park Hopper tickets. Given the high cost of the park tickets in general, though, Genie+ might be worth the extra money, just because A) you'll get on more rides, and B) a huge percentage of the other consumer suckas in the parks will have also paid for it, and you're in competition with them to get on rides.
Get to the parks 30-60 minutes before opening. That'll enable you to do more attractions before the lines get long. Take snacks and water. Try not to criss-cross the whole park, but instead do a bunch of stuff in one area before moving to another, assuming the wait times aren't terrible.
Pack in a lunch. The food in the parks is either "meh," or too expensive, or both. Plan for a break (or two) somewhere in the day. The parks can be sensory overload, so it's good to find a quiet place to sit down a relax for a few minutes. FWIW, there are some attractions that can also fit this role, like It's a Small World or the Railroad, or some of the indoor shows or rides like Turtle Talk or Pirates of the Caribbean. We've found it helps the mood to buy ice cream in the middle of the day and share it. Dole Whip is really yummy. If your hotel is close to the parks, it can be a good idea to go back to the hotel for a nap and/or quiet time in the afternoon. Often, the parks get less busy after dinner time.
Prepare yourself to get nickel and dimed. Park tickets are expensive to begin with, but then parking just got raised to $30/day, Genie+ will hit you with a $15-30/person/day cost, and there are a few rides where, if you want to skip the line, you have to pay (per person) an extra charge to use the Lightning Lane. And that's before you buy any food or souvenirs.
Large groups are hard to wrangle in Disney parks. Be willing to break up in to groups. Take a stroller, not just for the exhausted 4-year-old, but also to hold the diaper bag, packed lunch, etc.
Vegas: ignore the strip if you've got kids. There's not much there for them. The fountains at Bellagio are fun to watch, though! If you like Indian food, Delhi Indian Cuisine on Maryland Parkway is really, really good, despite the humble outside appearance. If you like Tex-Mex, it's hard to go wrong with Cafe Rio. But in general, Vegas is a city designed to suck the money out of you.