If it was only me, I'd be happy with a smaller place. If I had the money, I'd help them all buy homes, as their echo boom generation will drive prices up again. But since I can't afford that, the idea of being able to buy a home that would accommodate all of us if needed, for little more than I pay now, holds some attraction.
And if I found myself 5 or 10 years from now alone in that large house, I'm the kind of person that would move in a couple of roommates or take in old friends.
I think this is the key thing to think about. If you are committed to living in an intergenerational large house with a pool as a dream lifestyle for the long haul, then perhaps the listing you're looking at is a sane way to meet that goal. I think what people are reacting to, beyond just the usual MMM "don't pay extra $ for anything!", is that your general description, on the surface, sounds like a temporary challenge that you're trying to overcome with an overly large solution. Buying and selling houses, and moving, is expensive and a lot of work, and it's best done rarely. So how do you see yourself living in 3-5 years? Would this still be what you wanted? Or if the market tanked, would you have an overly large white elephant on your hands?
If you are genuinely wanting to create a home that your sons won't have to leave, that you and your mother will comfortably share for a decade, and that, should anything change with anyone's lives, you can both afford and be comfortable renting out rooms in because you love to have lots of people around you and good roommates are easy to find in your area, then, hey, go for it!
Have you gone and walked through this house? If it's niggling at you, I would go visit it. Homes feel very different in person than in our imaginations, and you will know immediately if this 4000 sq ft feels cavernous and wasteful. Layout, etc can be everything. Utility costs and pool maintenance are not small things, and mcmansion homes are often very poorly constructed. Beware of huge open foyers with vaulted ceilings, for instance! :) Then there's furniture for all the new spaces, etc.
Do consider carefully, though. Remember that homes designed to give everyone their own spaces mean that families spend much less time together, crossing paths, etc. It's a very different rhythm of life, where everyone is more independent. That can be good, especially if the goal is long term comfort together, but it can also backfire if the goal is more direct support and contact for your depressed son, for instance. Both of your sons right now have some mild discomfort in lack of space that provides motivation to move on. That motivation would likely disappear with a larger space and more privacy. If that's what you want, again, no judgement. Leave the house to your Asperger's son in your estate, and he can rent out all the rooms as a supplement to his own income?
FWIW, my mom and husband and I have just finished renovating a 2500 sq ft home to suit the three of us for the long haul. It's ridiculous luxury of space, and it's weird figuring out where we will all spend our time. We definitely hide in our own private spaces, and hang out less together. But, as mom is young and active and we all do want independence from each other, and plan to live together indefinitely (15-20 yrs for sure, unless something dramatic happens), it feels well worth it. Financially it was a reasonable, but not totally optimal move, but because of the long timeline, we're ok with that. YMMV.