You are wonderful!
As a stepmom, I would have to say that love is not something that can be measured. A stepmom can love her stepchildren with all her heart. Would I die for my stepdaughter? Absolutely! It doesn't matter if I gave birth to her, she is a gift from God to M., and I intend to fulfill my side of the responsibilities. I am not out to replace her mother, but someone has to fulfill some her needs when she is at our house. So that's M..
I really believe that it's up to the CHILD what they want to call the grown-ups in their life. A title should not be forced, nor taken away.
I can imagine, that if a child wanted to call her stepmom "Mom" and then her bio mom said "no way, that's MY title!" Well, you've J. shown yourself to be selfish in the child's eyes. You aren't protecting your job or title, you're HURTING it in the eyes of the child. Congratulations, the child now thinks less of you.
I have never tried to take the title of "Mom," although my SD sometimes calls M. that whether for convenience (my mom and dad are here) or because she's truly feeling it. However, I do wear the Stepmom title with pride. I'm PROUD to be her stepmom, and proud she has two moms who love her and care for her. My only job is to make sure her needs are being met, and that she grows up to be a lovely young woman (and she's already on her way!) I really don't care what kind of a title she gives M..
However, I'm sensitive to the fact that her bio mom may be offended if she calls M. "mom." So she doesn't in front of her. It doesn't bother M.. I'm happy to step aside for her mom. And I do try to make sure she has a good relationship with her mom.
I think if everyone involved was less concerned about titles (as you say) and J. though of the child and what they need, everyone would be happier. You're right, the child did not choose the situation.
I also think that "Stepmom" is a perfectly good title. It's tarnished a little bit by the reputation of "Wicked Stepmother" but we know that not all stepmothers are wicked!
Also, how would you feel if you were a stepchild living in a house of bio children and your stepmom refused to call you her daughter because it was "reserved for the children that she herself had?" If the mom introduced you all the time as "These are my daughters, and this is my stepdaugher." And if you asked if you could be called a daughter and your stepmom said "No, that's reserved for MY bio daughters."
People would think that cruel, and very Cinderella. But it's okay to go the other way?