It's not that she doesn't trust you to do it right, and rationally I'm sure she knows that the car is fine, but there is a strong irrational human tendency (especially with women, myself included) to want to be "extra safe" "just in case" something happens. As for me, I have poor spatial perception and I know that things might look ok to me but I cut it too close and it turns out it wasn't ok after all. For example, in your case, I might think the car was just over the line but then the door would hit it. I wouldn't trust my own judgment and would feel safer parking it further back.
By extension, I'm terrified to be in the car with someone else driving. I always stop slightly early for a stoplight and keep good distance between me and the car in front of me. Other people drive much closer and stop just at the last second. I know rationally that their perception is better than mine and we're not really in danger, but to me it looks like we're constantly about to get in a car accident and I can't relax at all.
I'm guessing your mother is like me in this regard. So I would suggest that you don't think of this as her not trusting you. Think of it as her not trusting herself and not being able to relax unless she can see with her own eyes that the car is ok. And try parking further past the line - you know she's going to move the car anyway. Again, don't think of it as having to prove your ability or anything. Think of it as you are helping her relax and be calm. I'm sure she will appreciate it, and it will be less stressful for you if she's not always moving the car after you park it.