Ask yourself if you would market her as an "unknown quarter horse cross"
There's you answer. Her value will be as a show horse only. It does not matter what her damns other babies did if they are not the same cross, it matters who was their daddy?
Your tell was "If you don't sell her, you 'd breed her".
This is a very thinly veiled sales ad, and I would think that with the benefit of your parents facility, marketing your homebred, successful show mare should be very, very easy.
Is it possible that crossed with a lovely warmblood stallion she would have a very nice foal? Yes, it's also possible that it will look like it's grandpa who may or may not be a short necked, short strided, short pasterned quarter horse.
Now that isn't to say that you can't breed two lovely horses and get the same thing, and it isn't to say you aren't within your rights to take a chance on the crapshoot that is breeding. But if you then try to market your mare, post whatever kind of baby she has, minus a continuous show record, then you have just decreased her value. Even more if the baby is a dud.
Sounds like you have access to stock with nicer pedigrees for breeding, sounds like she would make someone a nice A/O horse. I'd sell first, least second, probably not breed at all, until I had my own place and didn't care what kind of a baby she had.
The problem with trying to get a quarter horse mind in a good mover is...
You don't get to pick what traits transfer. You might get a quarter horse mover and a hot warmblood brain. If you could accurately predict what a hot/cold cross would get you, all the breeders would be rich, and all the horses would be quiet, 10 movers with perfect conformation and be ammy friendly. There would then be thousands of them and we'd all own one.
It just doesn't work that way.