[Eternal]

So you've been together with her for 3.5 years but this was your first time going over to her house? I'm a little confused by that. Has her mom known you have been dating this whole time? If she hasn't, then that may be why she thinks you don't love her. She may think you just want to have sex with her.
I think one thing you need to remember here is that nothing actually did happen. You just really scared her mother, so she's treating you both like something had happened. It's normal to feel tempted even if you're religious, but remember you didn't go all the way so you didn't do anything wrong.
I think you should talk to your girlfriend and see if her mom will allow you to come over for dinner so you all can talk. Then you can try and reassure her face-to-face that it won't happen again and that you feel really guilty about it. It will probably take time before she begins to trust you two again, but I'm sure she will once the shock wears off.