You need to slow down. Dude, you spend way to much time thinking, emotionally connecting with this stuff and trying to make everyone happy. If a perfect world did exist, that would have been possible. But guess what? A perfect world does not exist. And you cannot make everyone happy. That's a fact.
I don't like that you spend all this time thinking about your parents and about the fiance. Where are you...?
If I am understanding this correctly, your fiance made her choice to move to your town because of school. No one should feel obligated, whatsoever, to her because of her decision.
I do think that she is overreacting. She cannot have expectations that your mother will fill up her mother's spot. With time, maybe. But I think that it would be a lost cause if she enters a relationship with your mom with those expectations. There is some growing to do on her behalf. As some of the conflicts between her and your parents could have been simply avoided. Your brother's wedding - big deal whether your parents want to see him or you get married first. The fact that matters is that you both want to get married and spend the rest of your lives together. Everything else is a bunch of details, no one cares for.
Also, your parents are out of line as well. They sound like more traditional folks to me. It will take some time for them to accept that you have become a man. But YOU need to show it to them.
Here is the bottom line: if you are convinced truly and wholeheartedly that your finance is the woman you want to spend the rest of your life with, the woman you love with all of her weaknesses and drawbacks, the woman you want to bear your children, the woman that makes you, has always made you and will always make you happy - then listen to her! Make her feel confident and protected. Eventually your parents will suck it up. Because guess what - you will spend the rest of your life with your wife not with your mom. This is human nature. Honestly, where there is love, there is always a way. You should not be having cold feet as a result of the first hardship that you both face in your relationship. What would happen tomorrow if you have kids and they get sick, and you need to provide. Or if one of you loses their job or gets cancer? What would you do then? If you are questionning the future of your relationship with your fiance now because her and your mom don't get along, then I truly think that you should reconsider whether you are emotionally ready and grown up to be married.
Don't ever allow the comfort and happiness of someone else impact your own happiness. Even if it is the one of your parents. Parents will always find a way to forgive you if they see that you are happy. Focus on the relationship you have with your fiance instead!!! Good Luck.