As a coach and gymnast I agree with Geoffrey and Lasswadecoach. Although technique is learned over time it is important to stress proper technique from the very beginning. Lasswadecoach is correct when it comes to the technique that your daughter is using. I don't mean to sound harsh, I just don't want to see her get hurt and I want her to be as successful as possible!
I tell my girls that I'd rather see them do it correctly and fall or not complete the skill than do it improperly, slopply, etc and make it. As long as they try to use the proper technique. When I started working with the group of level 4s that I work with now, they had been moved up too quickly and they were not ready for competitive level 4. They could not do handstands without arching, or straight arm handstand forward rolls; they didn't even walk down the beam with straight legs.
It is VITAL to perfect the basics before moving on to harder skills. The harder the gymnast works at perfect technique on the basics the eaiser the harder skills will come.
Personally, and I don't mean to sound harsh, but I think that if your daughter wants to compete soon, do well, and go far in gymnastics, that the coaches, and everyone involved in her gymnastics need to focus on correcting the improper technique and form. In order for more difficult skills to be done correctly and without injury the basics must first be perfected--even if the gymnast is 5.
With my girls I stress that they are not too young to be good gymnasts, all they have to do is learn how to focus and think about what they are doing.
It seems that your daughter is working hard and that she has a lot of potential! I suggest working on form and technique at home and maybe mentioning something to coach...as to why your daugther may still have bent arms and legs on her backhandsprings when she's been doing them for a while (something to that extent).