I'm Unitarian-Universalist. I wouldn't do it. I would be very gentle and respectful to MIL but I would still refuse. I've been fighting this with my own mother, since DD1 was born more than six years ago. My mom is Roman Catholic, and truly believes that my children are destined for eternal damnation because they haven't been baptized. She believes it with her whole heart, and is genuinely torn to pieces about it- her motivation is entirely out love for my kids. But I still had to refuse. To allow them to be baptized, I would have had to stand in front of a Catholic priest and promise to raise them Catholic, and profess beliefs I don't hold, and I can't do that. Not even to help my poor mom sleep better at night, I can't. I don't believe in a God that damns innocent children because they haven't been through a ceremony with some water, and I won't say that I do.
It's been very hard. Mine were dedicated in the UU church, and she came, and was extremely polite to everybody and behaved beautifully, and then went outside and sat in her car and cried. It's been one of the hardest things I've done-- to have to refuse her this. But I have to, because I can't make promises I don't intend to keep. Finally, a few months ago, I had it out with her, and got her to realize that we can't keep dragging this up all the time-- told her she had to stop asking, or we were going to wind up avoiding her and none of us want that.
I would say you have to think about your own personal boundaries. You have to think about how sincere your objections are, and just what exactly you'd be pledging, and talk to MIL about her reasons for wanting this so much.
As far as the behind the back thing- I think your MIL would find it's not easy to find a priest or minister who will baptize a young child without the parent's permission. I found out a Catholic priest won't do it. My mom went and found out that "in an emergency," anyone can perform a Catholic baptism. I told her if she wanted to baptize them herself, I was fine with that if it helped her feel better. I just won't stand up and make promises I can't keep.