I want to do gymnastics, but my parents won't let me..?

I'm 12 but 13 in August, is it a bit too old to do gymnastics? I've always wanted to do it when I was younger but my parents said no because it would make your shoulders look ugly... I'm guessing they're saying really muscular arms. I've recently started practicing and working out more to gain flexibility because my friend showed me a back walkover. I only want to do recreational gymnastics and not compete. And I don't know if my parents would let me cause I'm already taking piano and thats about $50. I can do a cartwheel, round off, a backbend, and almost a front tuck on the trampoline. Am I too late to join? How much is recreational lessons usually? How can I get my parents to get me into it? And will they put me into a younger age group because I am not experienced? I really don't want to.. that'd be quite embarrassing.. Or how can I learn to tumble at home?