2 to 3 weeks? I think I need some clarification on this…if you’ve ordered a car, surely you don’t have to give your current one back BEFORE your new one is ready? This happened to me in the ’90s when a Ford dealer screwed me over and I had to return my current car and wait 2 months with a car until the new one was delivered. As a wheelchair user I’ll be furious if we go back to this. SURELY Motability will allow you to keep your current car if you have one on order.
Providing you have ordered a new vehicle before the current contact ends, Motability do usually agree to extend the contract until such time as a new vehicle arrives. (In the contract this is covered as it is ‘with the agreement of Motability’).
I think the OP was asking Motability about an extension without having ordered a new scheme vehicle prior to the current contract ending. Motability might agree to give the outgoing customer a few weeks but it is by their agreement and at their discretion as it is not part of the contract.