Try the motor mover again, this time properly. If it works then you probably have not done it any damage. These things are usually over engineered and can take some rough handling.
If you have damaged it, they are easily repaired by a service engineer.
------------- Lobey.
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I have done the same with my mover in error - glad i am not the only one! My hand brake would not allow the van to move. All that happened was the rollers on the mover spun against the stationary road tyres causing a small amount of rubber to be removed from them. So now i engage the mover before i disconnect the van from the car, or before i lift up the corner steadies. This avoids the need to put the had brake on. If i do not put it on, i cannot forget to take it off again lol! My mover is a powrtouch 1 axle heavy duty - i would recommend one to anybody - so much easier to push a button than push a van hehehe!!
Something I always do is as soon as I engage the rollers I put the socket on the drivers seat or near the pedals to remind me to disengage before I get back into the car to drive off.
You should get your brakes checked. As already touched upon in an earlier post, the mover should have slipped against the tyres if your brakes were working properly. This isn't brake damage caused by using the mover with the hand brake on, but I suspect your brakes are not holding as well as they should.