I can understand your parents' position -- it is highly inappropriate for a member of university staff (faculty?) to have pursued this kind of close personal relationship with a student. The relationship may not have become physical by the point it ended, but it was definitely headed that way. Yes, you screwed up by using the login information and that probably is enough to get you expelled, but the other person also violated policy by giving it to you (among other things) and should be held accountable. If the person returned your feelings, he or she would have stepped in to explain the situation and to try and protect you. They didn't. This person does not deserve your loyalty.
You may need legal advice, however. If it had gotten to the point that the person's supervisor knew what was going on and that person didn't start an official inquiry, then the college is probably hoping that you -- and the problem -- will just quietly go away. The problem with this is that it leaves this loser in the position to continue trolling the academic waters for more trusting and naive undergrads.
I don't mean to sound harsh, here. At your age, I very likely -- make that most definitely -- would have fallen for this kind of thing. I would have been horribly flattered and wouldn't have had the experience or maturity to recognize that the relationship being offered was inappropriate. I imagine you don't, either.
As far as the expulsion goes, you may have to just chalk it up to experience and move on. Make an appointment with an admissions councellor at the next institution, maybe with someone from their office of mental health or whoever handles students with disabilities present to explain about autism and some of the social ramifications of it, and be open and honest about what happened. Let them know that you now understand that you shouldn't use someone else's login information even if they give it to you. I can't guarantee that it will work, but it's about all you can do at this point.
But, definitely, file a complaint against the staff member who got you into this mess in the first place! And, in the future, if someone offers you a relationship that has to be kept secret, it's not romantic. It's a bad situation. Walk away.