I only have 2 kids so what do I know?

but yes, it is doable.
How many days? Just DL or parkhopping? There are a zillion things to do and not riding some of the rides should not be even a small turnoff to going!
IME kids are allowed to ride together on many rides before age 7 - or 14.
I'm assuming OP's little 2.5-yr-old is under 40" so I left out the big rides....
Of the ones mentioned so far,
For Ariel they were calling for people to divide their parties into 2s, 3s, and small 4s on our last trip, so all 4 of you should be able to fit in one car. My kids have almost always ridden this together - I just looked up when this opened and my kids were 4 and 7. I go in the car behind them, no issues ever.
My kids have been riding Buzz together for years - way before my oldest turned 7. Again, I go in the car behind them.
Same for Toy Story.
I agree with Starshine on HM and Peter Pan - DH, myself, and both kids used to fit in HM buggy and Peter Pan ship, and they do allow lap sitting, so you should all fit in one buggy/ship for both.
Other rides my kids have ridden together in a car on: Mater's, Luigi's, Jumpin' Jellyfish, Gadget Go Coaster.
The only 2 I can think of that may not work for you are Astro Orbitors (but doesn't hurt to ask!) and the bumper cars (where they are consistently picky about a kid under 7 riding with older sibling - that's probably why you see a lot of awfully tiny "7"-yr-olds driving.

)
Anyway, I believe the 14 age requirement is applied more often when kids want to ride with a younger sibling with no parent on the ride at all. In our experience CMs are happy to let little kids ride in their own car.
Go! Have fun!
ETA: OP's 7-yr-old may be very excited to be able to ride in his/her own car, so it may not matter at all!