Let me get this right: Your fiance’s mother is opening the bedroom door to “check on” her son? Is she worried he’ll be abducted by aliens? What if you two were having a bit of afternoon delight??? At 30, it’s long past time for an adjustment in their relationship. In fairness, she may simply be continuing an old habit. Apparently this worked for your fiance and his mother for a long time. But when things are different, they’re different. You are now an important part of the equation.
Start with your fiance. There’s no need to blame or be angry with his mother or to be upset with him — at least initially. She doesn’t see her behavior as unusual. He apparently sleeps through her intrusion so it may be new information to him that you are bothered by her visits. For those reasons, I suggest you focus on your needs for privacy and uninterrupted study time, not on his mother’s lack of boundaries or their unusual arrangement. Ask him to talk to his mother about making other plans for her lunch hour now that he’s engaged. She can keep the key for emergencies but he should be clear exactly what an “emergency” is. (Not having a place to go for lunch is not an emergency. Being locked out of her car when there’s a blizzard is.)
If he can’t do that, your problem is with your fiance, not with his mother. Marriage and making a life with someone means shifting our primary alliance from our family of origin to our new family in the making. That doesn’t mean that love, concern, and caring stops. It doesn’t mean that parents can’t be an important part of our lives. It does mean that there needs to be some boundaries between the generations in order to let the new family figure out their own rules, rituals, and routines. This is not something to be offended about. It’s part of the usual cycle of life. My guess is that your future mother-in-law went through a similar transition when she first married.
If your fiance feels he can’t talk with his mother or if his mother sees this as a reason to hold a grudge, you have another problem. You are then confronted with the strong possibility that to marry your man means to accept his mother as a part of the daily package. Only you can decide if it’s worth it.
I wish you well.