I don't think this is about religion or cultures at all really. You're allowing you're children to wind her up, and she is retaliating.
If you really want to bring your children up to have a healthy respect for both cultures then why on earth are you allowing them to taunt her!
I think sometimes in a mixed relationship you have to accept that things might not always be particularly fair or smooth running, especially when it comes to special occasions, and you just have to make the best of it! Coming from two so different cultures there are bound to be clashes but being petty isn't going to help anyone. For whatever reason she finds it hard to say it, and I think you should accept that, use it as a chance to illustrate the differences in religion to your kids and try to teach them to respect that!