Vehicle rental and parking will cost waaaaayyyy less than you'd spend on rooms at Disney, even if you stayed at a Value resort. To be honest, you'll come out ahead even if you forego that vehicle and just use Uber/Lyft.
Take the free room at Wyndham Bonnet Creek, and enjoy spreading out in a suite rather than being jammed into a room. I bet your kids will LOVE the water features at Wyndham Bonnet Creek much more than Disney's offerings. Unless you were planning to stay at a deluxe resort, the Disney pools won't be anywhere near what WBC provides (and even if you do stay at a deluxe, the pools might not be as good, depending on the resort).
Plan your park days so you are at parks that don't have EMH, and crowds should be manageable. There might be a few headliners you can't get FP for at 30 days, but those are the same FP people have trouble getting at 60 days (SDD, FoP, 7DMT), so no guarantees even if you spent the money for an onsite stay. To my way of thinking, those headliners are usually one ride, maybe two rides, per park. You can always ride them at rope-drop, park close, or just suck it up and wait standby (it's only ONE ride after all).