She has it. Like others said, she should not be doing it on her bed, but she isn't landing on her head. She has the fundamentals. The coaches were right. She is on a good track to learn it. It is no where near horrible.
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.