I'm still in the early stages of everything for myself (Very similar to you but about 10 years older). I can't comment on how or when to transition, because for one reason or another, I always felt I wasn't able to.
But 5 years is a long time to just save every single dollar that you get. Things come up. Car wreck, new housing, health insurance or even just clothes and personal items.
Plus you gotta factor that after your done with school, your going to need some cash to setup housing and transportation before you start your new career. If you don't do this on your own, you are going to be relying on your dad, which will keep his current hold over your life.
While I know it doesn't make sense, consider paying your own way in terms of food etc... Instead of having your family do this for you. The longer you let that happen, the longer they will have some kind of "control" or at least something to "hold" over your head. The faster you can be a complete "adult", the faster your decisions will be your own.
Plus, I know $35,000 seems like a lot, and it really is, but over the course of 5 years, I think your independence would be much more valuable. Remember, anytime someone pays for anything for you, it's giving them the go ahead to comment on your life.
Do everything you can, not to let someone have that power over your life.