Yup, I'm with the majority on this one. That really sucks but I think the email will just make it worse. If anyone says anything, it should be your FI. It's his family and I think it's best to let him deal with it.
You will have a beautiful wedding and hopefully she will come around and realize what she will miss by being this obstinate and change her mind. If not, don't let it ruin your day. No wedding is perfect and you can't control everything. Just keep your spirits up, be positive and trust that everything will be all that you and your FI hoped it would.