You are going to hear this from most coaches but we would generally recommend that she does not practice a skill that she is still developing at home, or in an air may and not with a parent spot.
It’s admirable that she is a dedicated gymnast and wants to improve her skills outside the gym. But when they practice in the gym their coach can watch each one and quickly correct errors. At home this doesn’t happen and errors can creep in, then the gymnast practices the mistakes and they become ingrained. It’s much harder to fix and ingrained mistake than it is to teach a skill from scratch.
I will tell you corrections that I would give the skill but each coach will want different things from their gymnast, as I am not her coach it may not be what her coach wants.
If she was my gymnast I would have her start with her arms at horizontal directly out in front of her, rather than to her ears. The arms need to swing enough that they hit the backwards horizontal before swinging back up to the ears.
By starting with the arms to the ears, when the timing is correct there is not enough time to powerfully swing them backwards to horizontal and then back to the ears. This means she will have to compensate by not swinging her arms enough or at the wrong time. This causes the back handspring to shorten.
The other things I would drill with her are lots of nice straight handstand holds, pushing up through the shoulders and handstand pops and lots of courbuettes.
From the angle of the video I can’t see her knees in take off. But a common cause of the undercutting back handspring is allowing the knees to come in front of the feet on push off or going up into the toes.
Watching videos of gymnasts doing real good quality handsprings can be valuable. It’s a form of visualisation.