You are not as mature as you think you are. You are trying to avoid taking full responsibility by suggesting you only said you’d “do your best” to avoid sex, not that you gave your word. You then put blame on your girlfriend for being “stubborn”. Really? The father had every reason to believe that you were making a promise. He extended himself by allowing a visit and you did betray his trust. As the older person, it was your job to withstand your girlfriend’s insistence.
Your girlfriend is younger than you are. Her parents are only doing a parent’s job by being protective of her. Although her dad may be mistaken that betraying him means you would betray her, he does have grounds for wondering when a promise from you is meaningful.
I think it will take a long time for her parents to want to support your relationship again. Trust is one of those things that is hard to win and easy to lose. You and your girlfriend can try to repair the relationship with them but it will require that you both take full responsibility for breaking their trust. You will also probably have to accept that the only visits will be highly supervised.
You’ve had a hard lesson in what it means to be trustworthy. I hope you can learn from it.
I wish you well.