You have two teenagers. Will they be willing to share the sleeper sofa in the living room? The bedroom in the renovated cabins have a queen bed and a bunk bed. The bunk bed will be fine for your three year old daughter, but probably a little small for your 15 year old. The cabins are moderate level resorts and I don't believe they include a Graco pack and play, like the DVC villas. The bedroom is very tight, which will make placement of the crib an issue. Plus, the bathroom has only one sink and it will be a challenge for 5 people to share, two of them teenagers. Disney has completely changed the kitchen in renovating the cabins. Gone is the full range...you now have a two burner cook top and a convection microwave.
Yes, you can park right at your cabin. But rent a golf cart to get around the resort...there's a spot to also park, and charge, your cart. Reserve it in advance as they go quickly.
I would check out videos (Allears.net channel on YouTube is a great source) of the cabins. Yes they are advertised to sleep 6, but I think Disney means parents, two kids and grandparents. You might find it a little tight for your family.
All Star Music has 25 family suites. They merged two rooms into a suite. So you have a living room area with a pull out sofa, sleeper chair, TWO bathrooms, and a small kitchenette with frig, sink, microwave and coffee maker. What they did was cut an opening between two rooms, turn one into a bedroom with a door, took the remainder of that room and made the kitchenette (and it's big). Or you could try one of the family suites at AoA. Bedroom with bath for the parents and plenty of sleeping areas for the kids, with a second bath. And a small kitchenette.
Good luck!
Addition: The cabins are basically a one bedroom single wide trailer. And I believe they each have their own small hot water heater, which may be an issue if your teenagers take showers like my daughter does (hot and long). We stayed in a cabin before Disney started renovations. 4 adults - me, my daughter, her boyfriend and her best friend from high school. At that time, the bed in the bedroom was a double and my daughter's very tall boyfriend had to sleep at an angle to fit, so only one person in the bed. My daughter and her friend took the bunks and she said they weren't really meant for an adult. I took the then Murphy bed in the living room, since I'd be the one up early to make breakfast. And after those three took showers, I had to wait about 30 minutes for hot water. So consider that in your planning.