My mother keeps telling people that she offered to pay for my wedding - which she never did - what should I do?

It's your wedding and you can invite whomever you want. You can tell your mother she is welcome to come but you are only inviting the people that are close to you and your husband and it is a small wedding. I paid for my own wedding and I knew how much money I had and planned my wedding according to that amount. I wouldn't worry about what your mom is saying. I listened to my mom's suggestions and then did what I wanted. My mother-in-law wanted a band at the reception and I told her that I didn't have the money and if she wanted one, she would have to pay for it. It was never mentioned again. If someone asks you, tell them the truth. If they really know your mom, they will just write it off as one of her nutty comments. If they believe her, then they aren't your friend anyway. But don't worry about all the negative things going on. Planning even a small wedding is stressful without all the drama going on.