Here's what I see. BFF is really a sweetheart for coming to all your children's events, even the little inconsequential ones. She has no kids so of course, you can't reciprocate in kind even if you wanted to. Now she is asking for something which, on the face of it, is pretty unreasonable, but in the grand scheme of things, considering her attitude toward your kids and her participation in their lives, is really pretty minor. And it comes down to the principle.
You are put in the position of choosing to stand up for principle and avoid setting a dangerous precedent vs. offending someone who is so much a part of your life and really does go over and above in her involvement in the life of your kids.
I still stand by the idea that it's not reasonable for her to ask you to do this. However, only you can really assess how important it is to you and whether it's worth fighting or not. How badly will her feelings be hurt? Will it kill the friendship or just make her sad for an hour? Or something in between? If it really will make an indelible mark, is it worth that? On the other hand, will you always be resentful, having to pay ever time this comes up, and believe me, it will come up again and again.
Regardless of what we all say, only you know (or at least can guess) how giving in will affect you and how insisting she pay will affect her. You need to think that through and come to a decision on which will work best for the friendship itself, both from her point of view and yours.