Umm no. Sorry, you shouldn't be apologizing. It's effing rude to say someone is an ugly bride. I don't understand why your FI is asking you to apologize, you didn't do anything wrong. Maybe having a huge fight in front of everyone wasn't the greatest idea but when girls are pissed we usually just flip out and don't think straight. If your MIL was ready to apologize for calling you an ugly bride, then maybe both of you could apologize for the huge fight thing.
Still in my head I'm just like what a friggin bitch! Ugh, that's the rudest thing I've heard in a while! So sorry this happened to you, you really don't deserve the aggravation. PS: I'm sure you are a lovely bride.