Any hotel/casino, whether on the Strip or elsewhere, is going to have quarter slots. The distinction is that on the Strip, those slots don't pay well at all. You might not think this makes much of a difference, but it does. Plus, it's more fun to play a high-payback machine. Furthermore, pretty much any Strip hotel is going to have that gigantic sprawl problem you mentioned. You're right, they're not very disability-friendly.
The larger locals' casinos, such as Red Rock, M, South Point, Orleans, etc. etc. have all the amenities the Strip joints have, but at a fraction of the cost. They all have pools, and some are very nice indeed (Green Valley Ranch springs to mind). Many of them have game arcades, movie multiplexes, bowling alleys, etc. etc. And because so many of their customers are local seniors, their accomodations for disabled people are usually excellent.
Here's my recommendation: South Point. They have everything you want, including a large and very nice pool. While the property is large, it's easy to get around (and they'll provide a scooter). It has several excellent restaurants, including one of the last few operational buffets (not a trivial consideration when feeding three teenagers!), a movie multiplex, and the rooms are large and very nice. I can personally attest to the fact that their ADA rooms are well thought out, and they have quite a few of them.
Green Valley Ranch or the M might also work well for you. Definitely, you'll pay less for a room there than you would on the Strip. The only negative is that those places are somewhat isolated (as is South Point, to a lesser extent), and not within walking distance of other attractions like downtown or on the Strip. But they have everything you need to keep everybody entertained for a long weekend, at least.
