Its a tough situation darling. I had a similar one except it wasn't just a guest, it was my ex who happens to be my husband's best friend. My parents strongly dislike my ex and didn't want him at the wedding and really weren't happy that he was in the wedding, and surprise, the day of the wedding, my husband made him his best man. I didn't have any problems with it, my husband, ex, and I all get along great! But my dad was barely even civil to my ex, I think he spoke less than 10 words to him the whole day and he was even there to help set up before the wedding. I personally don't think they should give an ultimatum, I think its rude of them to because it is your day and you want to be surrounded by the people you love, not by just your parents pick of guests. Maybe write a letter to your mom about how much it would mean for both your parents and your friend to be at the wedding. A wedding lasts a few hours, and while it might be hard on your parents, I'm sure they could be civil for that long to someone they don't like.
I wrote a letter to my dad about my ex being at the wedding and asking him to please be civil to him and not cause a scene.