There are no connecting AoA suites. You'd have to have two completely separate suites, making it less appealing.
We've had 5 children our last few trips and will have 6 on our next. Since we got to 4 children, we've started preferring staying offsite. At the time of year we go, we can get a 5 bedroom, 5 bath home for around $200 a night, including tax and pool heat, at Windsor Hills. You could get even cheaper if you stayed in Windsor Palms or Indian Creek. Not only do we get a ton of space, but we have a full kitchen, a washer and dryer, our very own swimming pool and hot tub (makes a great kiddie pool if you don't turn the heat on), and a garage converted to a game room. Staying somewhere that we can easily come back for naptime and have the older ones be able to read in bed for a little while and then get up and do something fun without disturbing the little ones still asleep is invaluable to us.
Of course, there are always particulars that make some things better than others for certain families. We drive, so we have our own 12 passenger van with us and don't have to rent one. We also have food allergies, and while WDW is better than just about anywhere for food allergies, having our own kitchen is also fantastic so that we can have a little more variety and a little less hassle, not to mention saving money. We go when it's reliably warmer and know we'll be able to use the pool. We also get APs and do 2 longer (2 weeks or more) trips per year with them, so our parking is "free." And because we do go on frequent long trips, the extra transportation time (while extremely minimal) isn't a big deal for us. Really, I don't think we spend that much time on transportation, but there is always the chance that we'll go back for an afternoon break and decide to just stay in for the evening rather than going back. That's not a big deal when you spend a lot of time there, but it is a big deal when you don't go often.
We haven't rented DVC points, but I've looked into it. The reason that we haven't done it is because we'd have to plan too far ahead and wouldn't be able to cancel as easily. We don't usually book our vacation until 3-4 months before we go, and by then we probably wouldn't be able to get one 2 bedroom suite for a long period of time without switching rooms. (Plus with our longer trips, we'd probably have to rent from at least 2 owners.) It's a viable option, though, and if it does work for your family, it's definitely worth looking into.