This is exactly why we have banned even cartwheels, forward rolls, and backward rolls at home. Practicing them even slightly wrong was only reinforcing bad habits.
I don't think I could ban cartwheels, she does them everywhere. But OP, your gymmie is adorable. You've gotten a lot of good advice (and you probably had an inkling of what the majority of replies would be). It's so exciting when your kid gets a new skill. But practicing them the wrong way can be harder to correct. Even though my DD doesn't do skills at home, she's at the gym with me 6 days a week. It's not all gymnastics, she colors, plays with her dolls, etc, but she also spends a lot of time on bars. She knows what she's allowed to practice, so it's safe, but we've all noticed it can be so easy to pick up bad habits without a coach right there supervising.