You can only do what you can do, but I agree with others, try, TooManyViolinists had some great suggestions in terms of instruments and programs.
One thing to be careful about is judging your kid (or having her) against others. You are going to see a lot of kids who started young, who are doing concerto competitions (don’t get me going on prodigies, a word that should be relegated to the dust bin), you hear of all kinds of crazy things, kids from well off families doing lessons every day, and it can feel like it is impossible…and I can tell you that first of all, some of what you are hearing is kind of half true. I have heard parents saying their 10 year old was playing the tchaikovsky concerto (which is an advanced one to people not in the violin world), and I saw the kid playing it and, well, let’s be kind and say it was cute. I remember my son (he was like 11 or 12, had just started with a much higher level teacher) seeing this ad for a performance at some church, touting this like 9 year old girl doing a recital playing some sonatas and a concerto, how she made her carnegie hall debut at 7, etc etc…we looked it up, her carnegie hall debut was some music school in NYC rented out carnegie for a music competition (of their students) and she won it…and I know someone who went, said she wasn’t the cats meow, was another prodigy wanna be. You will see kids in competitions like the Junior Menuhin who are her age, and feel like 'wow, she isn’t anywhere near there". It is great to see the level other kids are at, it can be a driving force, but there are no rules. If you told me your daughter was 14 and just starting to play, I would tell you as gently as I could that that might be an insurmountable barrier (not impossible, my son met a cellist in grad school who started playing at 15, got into a really incredibly high level program and then was in the same master’s program as my son, so it is possible).
There is always a range of playing with students and what is it they say, past performance is no indication of future performance? This is really true. The hotshot kid winning competitions right and left in high school fizzles out. In the one competition my son was in in high school (NMTA nationals), he lost out to this kid he later saw at NEC, where he went undergrad, and the kid wasn’t that good. It used to amuse me to read some of the forums on the violin channel and other places, to ready stuff that I absolutely knew was bs from being in that world.
The upshot is that while it is important to know the level out there (and if you have a good teacher, they will know), and to do the best you can with things, the most important being that your D puts the effort into learning. One nice thing technology does is she can listen to recordings, my son used to spend a lot of time listening to the recordings of famous violinists to see what they were doing, and decide also what he felt was his style, not copying them, but rather the kinds of things that struck a chord in him. He says it really helped him dedicate himself to practicing, that it was interesting working to get that sound.
I also recommend that she may want to, if she already isn’t, to learn music theory. There are online courses out there and while music theory is something a lot of music students dread (my son loved it, still does), it can really help with understanding the music and how to play it.
Again, there is no golden path with any of this. I have seen high level students who didn’t do the summer programs and the like, and while I encourage you to see if there are ways you can afford it, I don’t think it necessarily is a blocker (that doesn’t mean that TMV is wrong, a lot of the kids getting into the top programs have done those things).
One thing I recommend she try is the New York String Orchestra Seminar. It is held in NYC roughly december 19 to 28. It is free in terms of tuition, room and board (you would need to pay for travel to it), and it is an intensive, fun experience, my son did it one year, it is run by Jaime Laredo. They do two performances at Carnegie Hall plus they do chamber as well. I think the youngest age is 16 to audition. It is very competitive, and isn’t easy to get into, but is an example of a great program that is free. It is something to work towards, and I think your D would love it. I also know they look for kids who are doing what your D is, they try to have a wide spread in terms of where the kids come from, and a variety of backgrounds.