What to if my girlfriend told me to come over to visit her at her father’s house, and now her father wants to charge me with trespassing?

Absolutely, you should fight this.  You have an excellent defense.  Trespass requires that you knowingly enter or remain unlawfully.

The father does have a right to bar you from his property, assuming that it is his (i.e. that he is the property owner or the tenant of a rental). However, since to be convicted of trespassing requires a criminal intent as well as the physical trespass, if you entered the home with an invitation from someone who lives there (even if she is not the homeowner or tenant), you would not have the requisite criminal intent and should have a good defense to the charge. If the police do contact you, simply explain what you wrote here: that your girlfriend invited you over and you thought you had permission; the police are unlikely to take further action.

Note the following:

1) If you did not leave after the father told you to, that changes the equation: remaining on the property after being told you had no right could subject to you criminal liability for "defiant trespassing," since remaining after you have notice that you cannot provides the necessary criminal intent.

2) If your girlfiend is actually an owner of the property, or a co-tenant on the lease with her father, or sublets (pays rent to) her father, then she *does* have the right, as someone with the right to possession of the property, to have you over and you would not be trespassing.

If you were invited to your girlfriend's father's home by your girlfriend and you were later charged with trespass by the father, you can fight the charge for the simple fact that you were induced to your detriment to go to the location where you were not wanted by your girlfriend.

Had you known that the father did not want you at his place, you would not have gone. I suggest that you consult with a criminal defense attorney to further assist you with respect to the criminal charge that you are facing.