Even if you are looking towards marriage, it can be better to hold off on more serious activities until a couple of dates to make sure you both feel the relationship is moving in the right direction. She found the perfect Mormon guy, they were married in the temple. She hasn't submitted the paperwork yet but I have no doubt that she will do this eventually. Anyway, you got yourself a treasure. Also, they are encouraged to date in groups and not pair off alone, so if your date insists on the same, then agree politely.
Are they a functioning member in society. All these are reasons to have some serious discussions. The Mormon culture has mastered the forked tongue. It has worked and my children are very protective of their father. Unless you convert she won't marry you, plain and simple. I'm in the exact same pulling-out-my-hair situation that you are. Going along with her cult might feel fine when it is just you in her, but if you have kids, it will be very different. What can you expect. Religion is super important to LDS people but there's also alot of exmormons.
After my divorce I dated Mormon men в disastrous. And no one has the right to judge you for your decision. Of course he invited me to come with him, but he is in the wedding, so I'll be sitting there watching him in the wedding on my 30th birthday weekend. I'd gladly give it all up to have him and feel wanted. At the risk of overloading this post, I'm going to copy and paste here, a Reddit comment that I made in this exmo sub the other day. If you and she are sealed in a Mormon temple, your children will be can be sealed to you. Every new set in our ward looks at him as fresh meat. A straight-laced, returned sister missionary, raised in the cult, and in family of similarly entrenched cult members, will not likely remain happy with a non-member.
I would advise you to try to be as understanding as you can of her point of view, because having you world view shattered is very difficult and can take a long time to recover from. I've luckily broken down my GF's defenses about the church a little bit. My experience with non members has been so much more meaningful and caring.