I get your hesitation - they aren't paying, so why give them the recognition? On the other hand, the invite isn't necessarily about giving them recognition for footing the bill. It's about the celebration of your wedding. Maybe the way you might make everyone happy is rather than put your mom's name on it, put "together with their parents" or "together with their families" ...something like that. No names, but some recognition that they are happy for you.
By the way, be careful about what you are willing to give up to make Mom happy. Because if you really don't want to include her name, doing so without making a big deal and pointing out that it's not what you want to do will just encourage her to make you accomodate her on other things.
Good luck with this. Just remember that it's YOUR wedding. You've waited this long, there's no reason that you have to compromise to make people happy.