So by working "good" and "bad" legs, the gymnasts build their strength on both sides? I never knew this was even a thing! My DD just works her good leg. The bad one gets ignored. She said she just does the side that feels natural. Does this sound atypical?
When starting out, what feels 'natural' may be a mix (like your DD and mine). To build the skills with proper connections later, it is important to have a dominant or 'lead' leg so that you end up on the correct foot / direction to go into the next skill (as I understand it). Maybe a coach can explain better.
Training both sides (like raenndrops described) equally is, I think, less common, though certainly would make for a very well-rounded gymnast. Gyms we have been at have just had girls train one dominant 'side' for skills. I'm sure there are gymnasts who are equally good with skills like leaps on both legs. I just don't think it is super common.
Like yours, my DD originally did her back walkover with the 'wrong' leg and had to switch. She also did her splits and jumps 'wrong' compared to the way she naturally did a cartwheel and roundoff. So she kept the cartwheel and roundoff lead foot as 'dominant' and changed the back walkover, jumps, and splits. She can still do a back walkover and splits with either leg, but her leaps and jumps are far better now on her dominant side (that she switched to).
My son also has a little mix. To this day, he hurdles onto the vault springboard with the opposite leg compared to how he hurdles into floor tumbling. It works for him, though, so coach has not asked him to change it.
I think your DD will be fine! Just takes a bit of time, but if she is dedicated, she can adjust.