Holding your fingers properly as you play piano is very important. It’s as important with any instrument, for that matter.
I’d just like to point out a few things that affect finger position for piano.
First, posture is a big deal. It’s very hard to play properly if there’s any slouching going on. It’s not a good habit. The reason is that it pulls the wrists down. The arms get “heavy” as you slouch and the wrists find themselves resting on the keybed (the little piece of wood that sticks out past the keys). In turn, this pulls the fingers down so that the fingers are nearly flat on the keys. Try and sit straight with shoulders down.
Ultimately, this refers to how high the elbows are. If a child is too low, she has to reach up to the keys. This is basically the same resulting problem as slouching, but the child cannot do anything about it. Her posture may be perfect. The solution is to give her something to sit on.
A related issue for children is that they have nothing to rest their feet on usually. They typically just swing above the floor. When she has something to rest her feet on, her lower back is actually supported better, which results in more confident playing. She will play more confidently when she is not (subliminally) distracted by trying to hold herself up differently. Comfy is good.
This is actually probably the biggest one (as I’ve mentioned before). When you’re stressed, muscles are tense, and everything travels north. Shoulders go up, breath goes to the chest, and fingers go up. Take some breaths and relax. If you’re too stressed, get up and walk around a bit. It is hard work to train your fingers, and can be frustrating. Keep tabs on your turmoil.
Finger position is important. Give them every opportunity to succeed by watching your posture, height and stress level. Then give them time. Keep working at it!