You're not alone in your feelings. I'm in a very similar spot. I don't suggest coming out until you are independent. Transitioning certainly won't help your relationship with your dad.
I know what it's like to want to make your parents proud. When I was in middle school I was very over weight and sick all the time. Since I was absent all the time I was no longer the successful student or athlete my mom could brag about. She would complain about me being too fat to fit into the stylish clothes. She would even complain about my hair, which was falling out. I could only style it in one way to hide the bald spots. She sent me to therapy, not because I had issues from being ill, but because I wasn't boy crazy like she was, no wonder she had me in her teens. She has the worst judgment. The therapist wanted us to work on our relationship and we were supposed to do something together once a week, sharing our interests. Since I was trying to lose weight I had been walking at a local state park. I took her there and she complained the whole time and ended up ditching me to go on a date with some guy she had met online. To her I was just a stupid and ugly embarrassment. After my hair had finally started growing back she clipped some of it for a drug test. Then she didn't even care when she found out when I actually was.
In her 30s she started to get a lot more mature and our relationship improved. After she met my now step dad it improved even more. He is very level headed. I'm honestly shocked how much she has changed. I made the mistake of coming out to her recently. She was seriously thinking of disowning me, but she never worked up the nerve to have to talk to my step dad about it. We are pretending like it never happened. I found out a few hours ago that she told my grandparents, who I'm living with, to not let me save money because I just plan on saving up and hurting myself with it. Transitioning is definitely not going to improve our relationship. It is not going to make her respect me more.
Even if you achieve things your parents want, doesn't mean they will be proud. I showed my mom the invitation from the honor society I got and all she said was "make sure it's not scam" since there's an initiation fee. Then when I invited her to the induction she said "do you have to go?" I've always had a strong interest in medical stuff. When I told my mom I was thinking of switching majors and going to school for forensic medicine she just said "Do you really want to be in school for 8 years?"
Transitioning feels like just a fantasy to me too. How I get though is trying to remain optimistic. That eventually it will get better. Right now it is possible that in the future I will be able to transition. When I feel suicidal I remind myself that if I do kill myself then I am taking away the possibility of transitioning. Then I really will never achieve my dreams.
Taking the steps to become independent and transition is very overwhelming. I suggest getting a job, if you don't already have one. Start saving. Every dollar in your bank account is another dollar towards transitioning. Working and being a full time student also can help distract you from your problems.
Hypothetically, if you do get T from your doctor. Do you have a plan for worst case scenario when your parents find out? It would be amazing if they were on board, but there is a good chance they won't be. I don't expect my mom to ever accept me, so I'm working on not wanting the conditional love my mother has for me and living to make myself proud.