EXACTLY

Spiritual guidance - that is what you during the baptismal servie are saying your vows to do.

What if you were to offer to take the child to church? That would be fitting in with your agreed responsibility while giving the mom the opportunity for a break they need? Just a thought.

I'm not sure the best way to approach the situation with the mom other than to be brutally honest about voicing your expectations. Of course, you can always say "No"