The birthday ride-on car causes a fight at the play area every evening

He turned 1 last month and my in-laws gave him a battery ride-on car, the kind with lights and songs. Every evening after daycare pickup, my mother-in-law wants it taken down to the play area in our building in Miyapur so the other children can see it. The other children do see it. Five of them, all wanting a turn, and my son, who can barely steer it, screaming whenever anyone else touches it. I spend half an hour refereeing and apologising to the aajis on the bench. I'd quite like the car to stay at home and for us to go down with nothing, or just a ball. But it was a gift, and I don't want it to look as though I'm hiding it. How have others handled the big present that causes trouble downstairs?