You do nothing. They legally cannot marry because they are not competent to make informed decisions. My daughter told me there was a couple in her facility who thought they were married. Both had living spouses that visited. You just have to enter their world.
I think you handle this as many als do. Elders often date and even have sexual interaction, and if they’re consenting in the moment and in their room, it’s not considered an issue. Marriage however is a legal contact that it’s unrealistic to hold dementia patients to.
Instead of a legal wedding, I would propose one of those “promise ring” ceremonies. Make it very weddinglike. It may just be enough.
Sounds like magical thinking, and not something you need to spend a whole lot of time working on. Worry when the facility reaches out to you with it being a problem. You do not tell us much about Mom, her diagnosis, her prognosis, how long in care, and etc. That might help us answer. Do know that this is not at ALL uncommon and that often couples think that they are, in fact, married, and that their visiting spouses are virtually strangers who are kind enough to pop in once in a while.
Instead of a legal wedding, I would propose one of those “promise ring” ceremonies. Make it very weddinglike. It may just be enough.