Exactly what others have said about having a frank discussion with your trainer. No sense in playing guessing games about why you two are disagreeing when you can just ask- what does she dislike about these horses? Does she understand YOUR goals and aspirations? How can you two get back on the same page, shopping-wise?
Personally, I would almost never advise a student to buy an unbroken 2 year old. You don’t know how the horse is going to turn out, even if you know his siblings- having ridden many half- and full-siblings, even ones brought along in the same programs, I can tell you that family similarities can be many or very, very few. If this is your only horse, it is a very expensive risk to take, and one that may seriously limit your riding opportunities for years (while still costing a lot of money). Unless it is a truly exceptional horse in just the right situation, I would always advise buying a horse the buyer can ride first, unless the buyer is very experienced or a professional.
The same goes for green projects- some are well-suited as project horses for competent amateurs, others need to be in a serious program. It is possible that your trainer does not think you are ready to take on the kinds of horses you are looking at, and is trying to steer you towards mounts that are more appropriate. How much experience do you have with green horses? No trainer wants to see a student stuck with an unsuitable mount, and many people don’t realize how green is too green until they are in over their heads.
With that said- if the above is not the case, and if you know 100% what you want, and your trainer isn’t on board, maybe she isn’t the trainer you need. If she doesn’t like your horse, she isn’t going to enjoy working with you two, and you need (and deserve!) someone who wants to be invested in your future with your horse. You can always find someone new who is excited to work with both of you.