FFBBT- like I said, just show them you are serious about it. You are still in high school, they might not have a grip on what your doing. Espcially since your father grew up yeshvish, he has his own hold backs.
You were born into the life you have, and you are there for a reason. You have an obstacle, but it is up to you to decide whether this is going to limit you or not.
In my story, I spent a whole year behind the scenes on my life, because my parents didn’t want to see it front and centre. You have to realize that they have their own life experiances and you aren’t going to change that. The only thing you can change is their perception of you. If you show them that you are serious (and by this I mean say to them, I love you, I love that you guide me and have raised me to make choices productivly. I feel that I have thought about this alot and going this path is the way for me. Here is my plan (just a rough plan): Im doing this schooling, this seminary etc. This is how I plan on paying for it (I’ve looked into loans, applied for scholarships, spoken to bankers etc.), because I would never expect you to pay. I want to give you nachas, I want to make you happy, but I also want to make me happy.).
FFBBT, it is showing them you are happy and mature. That means you need to accept them and learn to work around them, not the other way around. If you want to be YOU, then be you. No one is stopping you. Not even them. You just need to elarn to navigate your relationship with them, and that starts with forming a baseline of mutual understadnign between you guys.