Olivia, I'm sorry that you're dealing with all this at your age. It has to be rough. I know about promises made and broken by the people you are supposed to be able to trust the most. I was much more fortunate than many, having the mother I did.
There are a couple things I'd like you to think about. The first is that whatever you post on the internet stays on the internet. People often think of it as a safe place to vent, due to the anonymity. And it generally is. I think your original post has gotten the reaction it has due to the emotions you expressed. Again, I don't know if you meant them or not, and you are CERTAINLY entitled to your feelings. If you haven't already, I would strongly encourage you to talk to a counselor or therapist. Someone who doesn't already know you and have preconceived notions about you or your living arrangements.
And that leads me to the second thing I want you to think about. There are people out there that you can trust. The hardest part is finding them. I learned that one from three decades of experience. One of the people I trust the most is my therapist. I might not like what she's telling me, but I know it's the truth. I am that way with my friends, and while they might not appreciate it in the moment, they know that I won't lie and that I have their best interests in mind. I hope you can at least find some friends that you can talk to.
I am confused on one thing at the moment, and I'm sorry if you've already addressed it. I'm very tired. Is it insurance or agistment your father won't pay for?
Again, I'm sorry you're in the situation that you are, but I think you would be better served to not put things on the internet while you're so upset.
If you want to get things done with your horse, there are options. I missed why your horse is restricted to light riding. I hope he (she?) will be okay. If it's the cost of agistment he won't pay for, would a lessor pay for it? I know you said free lease, but it's an option. And if your horse is kid safe, it should be a very attractive option. You could have a conversation with your father without getting overly emotional. (I know how hard this can be. I'm still learning and I'm almost twice your age.) Maybe you could write a list of points you want to discuss and practice them before the actual conversation. Have all the research done so if he asks you a question, you can answer quickly and confidently. He still may not give you what you want or what he promised, and that sucks. It really does. I know you said you're in year 11 and you don't have a lot of free time for working a part time job. Maybe you could get together with someone and brainstorm ways to make the amount of money you need. Could you work off at least part of your agistment?
It sounds like you're going through the painful process of growing up. I'm glad you want to do what's best for your horse, and I wish you luck.
Learning never stops