Do you want to stop the tumbling? From an adults point of view I think extra curricular activities are A Good Thing, and I'd be worried you were going to hang around the house, or street corners with your friends. Also the exercise thing, I'd be worried about you not being as fit and healthy without that...
Can you ask your mum why she won't let you stop?
Is there anything else you'd like to do? Another sport? Dance? Or even some other hobby like music? Giving up gym will allow you to try a whole host of other stuff, and your mum might be more accepting if you tell her you've gone as far as you can in gym, but would like to give x a go instead.