Lots going on in this situation. I agree with @Mrs.Groovy that you have to be careful mixing family with business. But I’ve also had lots of good situations borrowing money from family without awkward holiday dinners. I think the key is to treat it like business and make sure everyone (you, your fiance, your mom) see it as something that meets their needs independent of the family dynamic.
And with that said, meeting everyone’s needs was the part that seems unclear to me.
Your fiance wants to buy something new. Why is that? That one needs to be talked about and explored first. And you want to buy your mom’s house. But is it a good deal? It’s more expensive and you could potentially get seller financing, but how will it move you forward in your financial life? And why not just keep what you have?
And if you do buy her house because it’s a good financial deal, why not just sell your town house in the city? Or sell both yours and his? Or why not buy hers as a rental and stay in one of the current houses?
Those are just initial thoughts. There is a lot to think about.
I personally like starting out with house hacking or live-in flips if you’re going to buy a house. As I showed in The Ultimate Battle of Housing, the cost of buying a regular old house instead of one of those can be hundreds of thousands of dollars in missed opportunity.