This has obviously escalated into a very serious situation.
The fact that her father has physically asaulted you is a federal offence. There is no way, under any circumstances, that such action should be tolerated at all. If this ever happens again I suggest you talk to your parents and talk to the police as well.
Rebellion tends to just add fuel to the fire and, like you said, running away isn't going to get you very far. Such extremes tend to be dangerous and risky and should be avoided.
If you've already tried having a reasonable conversation with your girlfriend's father then try to find a councellor at your highschool or local community centre and explain your problem to them. Perhaps they could sit down with her parents and explain your feelings towards the situation.
Sneaking around only makes things worse if you get caught, and it's really not hard to slip up and get caught, as you've found out the hard way. Spending time at her house obviously isn't productive for either of you, so why not try spending time somewhere else? Like outside or at your house? But do NOT lie about it or try to hide it. That would be enough to anger any parent and would only make it worse on the both of you in the long run.
Probably the sneaking around and secrecy of your relationship only angered your girlfriend's parents further. I've learned, from experience, when a parent finds out that you've been hiding something from them, they immeadiately become more suspicious and angered. Big mistake.
The best way to go about this is to hold a peaceful group conversation with you, your girlfriend, her parents, and your parents. Be open, honest, and, above all else, calm.
I hope things work out for you.
Smile, though your heart is breaking....
My crazy little universe....
"Whatever tomorrow brings I'll be there....
With open arms and open eyes...."