How are you not getting your bags? I hope you're not planning on DME getting them. If you don't ride DME from the airport, you can't use their luggage delivery service. For more information, there's a sticky at the top of the Transportation forum.
While I agree that Disney doesn't want us using DME just for our luggage, they certainly aren't doing anything to prevent it!!! They aren't even asking how many bags we have checked!!! They used to, but not anymore. So, in all reality, even if you're on the bus, and the airline misdirects one of your checked bags, how is DME going to know? They have no idea how many bags you checked and are expecting to be waiting at the resort!!
So, long story short....does Disney want you to tag those bags, and then rent a car, or use a car service, to get to the resort? No. Can you do it? Sure. But, read the sticky thread to get all the info you need to make an informed decision.
I doubt renting a car will give you all that much time.
Here are some times I've had.....gate to resort.....
DME.....checked bags.......55-85 mins, average about 75 mins
Towncar service...checked bags......60 mins
Towncar service....carry on only.......45 mins
Mears shuttle......90 mins
Rental car.....60 mins...at least.
It takes about 15 mins to get from gate to level 1, where you will find car rental areas. Then, 15 mins in line (possibly shorter, but I've had much longer times as well), 30 mins to the resort (at least).
The least amount of time is going to be with a car service, and no bags. Be sure you are completely informed before making a decision!!
Is there no way the parents can move their Sanaa ADR up a bit, say to around 8ish? That would work out much better.