I don't think it would be classed as abnormal, but it's up to you really.
From their point of view they don't want to give you the full amount and be unsure whether you will go through with your side of the deal and pay off the finance.
I can understand your concern that they only give you the difference and don't pay off your outstanding balance.
I would just check with the finance company that Glen Coopers have paid off the outstanding sum before you give them the car, and then accept the difference they owe you
