I'm sorry to say that you are not alone in this. But keep up the fight. Don't let her overstep. I fought and ended up with a very disengaged stepmom for my DD. No longer do I have to deal with teachers, coaches, dr.'s thinking that she's the Mom and who am I?! Stand firm, it works. Let people around the child know what's happening. Empower the kid to correct people.
Nobody can take the place of Mom. I don't even like the name "Bio-Mom" because is implies that it's some "kind" of a Mom, equivalent to a "step-mom" or something. Mom is Mom, nobody else.
I hope your child's SM backs down.