That's a great cartwheel for a 4 year old! Well done to her.
It's great that she has goals, but your job is to remind her that things will come when they come, that there is no hurry and that she is already doing well and working hard.
At this age (from what I understand), coaches are more interested in the child's potential than whether they have perfected skills. She will impress the coach far more by having an amazing work ethic, never complaining about conditioning, willing to give things a try and always being attentive and listening to corrections, both hers and corrections given to other children. THIS is what will get her attention. Although it feels like skills like the cartwheel are important right now, your perspective *will* change as time goes on. Most kids at 4 are no where ready to do a cartwheel at the level your child already is, this is why they are not spending a lot of time doing them. Also, they are less important than you think at this point.
I'm here speaking from the hugely experienced *cough* perspective of a mother of a 5 year old

But I watched her move to a higher level group with a cartwheel no where near as good as your daughters, hey she was moved to 12 hours a week with a cartwheel that wasn't in a straight line.
Those badges, certificates etc. are just to keep the interest of the parents and kids who will probably wander off after a year or so when they realize that gymnastics is far more 'boring' than cartwheels and handstands, with many hours of really really repetitive conditioning and drills. If your child is interested in higher level gymnastics, she pretty much needs to be the sort of kid who enjoys this, rather than getting annoyed that it's boring, and you have to be supportive of this.
You're in the UK, so she can't actually compete until she's turning 8, right? I'm sure there's no rush to move her to the next group (apart from wanting to say she got there before she was 5). Don't fall into the trap of setting deadlines for skills. By the time she is actually old enough to compete you'll be insane and she'll have burnt out!
Have a search on this forum and read the posts from people talking about their 3-4 year olds and listen carefully to the responses. You don't have to agree with the responses, but do read them. If you have trouble finding stuff, let us know and we'll find some relevant threads for you.
What you don't want to do at this point, is make the coach and gym owner wonder if you are going to be a "crazy gym mum" and cause trouble later on, particularly if you are worrying a lot at this early point. You will get much further by showing outward trust in the coaches, asking questions gently, not demanding your child gain those extra skills to be moved up soon and giving the impression that you are laid back about the whole process - even if you are not
