If her jumps are in need of improvement and her sprinting is limited, it sounds like she may need to work on her fast twitch muscles. There are a lot of drills for this, not many of which are very fun. I like using the jump rope to help this some. I try to make sure they are jumping on their toes without the heels touching the ground just to ensure the calves get the work.
For the level 4 vault, I have the kids try starting from 9 or 10 steps away from the board. They then start with 3 slow steps (I have many of them use "stupidly slow steps" like jogging in slow motion). After the 3 slowmo steps I have them jog a few steps then take the last 3 steps quickly and jump into the board. Many times the starting distance is the culprit with a flawed run. Adjusting where the gymnast starts and making sure they know where they start is an import part of the way I like to coach vault.
If everything works as one fluid run, hurdle, punch; you may eventually end up with a vault that looks something like this one:
YouTube - First competitive Front Front
If your daughter is having issues with a straight jump, I'm not sure what she'd need to do to work on it other than just shapes and making sure she pushes all the way out her toes when she jumps. Many people try to use just their quads to jump not realizing that the calves are nearly twice as strong.
I use the trampoline for working fast split jumps and straddle jumps. As long as they are focusing on form. Many kids will push the split jump past their point of flexibility and bend their legs or twist their hips. Flexibility plays a big part in the look of a split jump so making sure the split work is there is important.
There are many dance drills for split jumps and leaps, none of which I can actually spell since they all seem to be French. Mainly just working the skill until the body knows what to do.
