Where would you be driving them that they would need to take the scooters? If you stay on site, in a hotel on the monorail, and eat at WDW restaurants, what else are you planning? If you're going to an off-site restaurant could you park in handicapped parking near the entrance (or drop them off close by) and have them walk a few feet?
DH and I both rented scooters last January and stayed at the Grand Floridian. The room wasn't large enough to accommodate the scooters so we parked them in the hallway near the room. We checked with concierge and were told what to do. We kept the keys with us, so the scooters didn't drive away without us. I don't know where the Poly would tell you to put them. Our extended family has eaten at Ohana and loved it, and I would like to stay there some day. In January it was actually cheaper to stay at the Grand Flo. I've heard that WDW gives a 30% deluxe hotel discount to seniors over 60, tho we saved more than that by staying off-season.
We rode the monorail and buses, and never had to split up. When we rode the buses, it took longer to parallel park the scooters onboard, and the driver had to anchor them down (like seatbelts.) For the monorail we just drove onboard and drove off. Even tho the buses were a bit of a hassle, it was still simpler than trying to cram two scooters into a car.
The scooter rental place will caution your parents not to race each other. 8^) It's not racing if they're just trying to keep up with each other, right?