OP - I’m going to take everything you say at face value in the event that you’re representing everything with complete accuracy, but please reflect to consider if what you’re depicting here is the whole picture.
Per your details, you are a minor, and your budget is 60k. You want a warmblood, that can jump 3’6, and you’ve done B shows (though the last time you showed was at 2’9). Showing is a priority to you.
First: Identify the non-negotiables. These are your dealbreakers. Things like “We will not spend over $xx,xxx” are a hard line.
Second: Identify the things you can compromise on. You’ve mentioned several things (you want to show, you want to jump higher, you’ve shown 2’9, you’re jumping 3’3) that don’t necessarily contradict each other, but we live in the real world and sometimes we need to give up X to get Y, or give up Y and take a smaller x to get Z.
You could compromise on breed, age, height of fences, age/condition, etc.
Third: communicate! State your goals clearly to your trainer. (“I have shown X, I am schooling Y, I would like to progress to Z.”) Then ask what you need to do to get to that goal (“What steps do I need to take?”) Tell her what you have identified (“I recognize I will need to buy a horse since no school or lease horse is available that can do these things.”) and then ask questions. She’s pushing the stock horses. Ask her why. Ask her the pros/cons for that type of horse when held up to your goals. Same with thoroughbreds. Same with warmbloods. All of them have pros/cons, it’s just finding what you can get and live with.
Alternatively - I do think it is silly that you have connections at a show barn that seems to already be set up to do exactly what your stated goal is, but you aren’t utilizing that resource in your horse shopping. Not all trainer programs fit every goal. If your primary trainer isn’t in alignment with your goal (she runs “mac” but you want to do “samsung” software) rather than trying to code work-arounds, it makes more sense to just work with the people who are already doing exactly what you wish to be doing.
(That said, this is a good opportunity for you to learn to research, plan, and communicate.)