Things you need to know:
I have a son (gavin) and stepdaughter(belle).
They are only weeks apart in age.
I've lived with my step daughter since she was 2 years old (she's now 4).

Here's the issue:
My step daughter's mother was only in her life once every 3 months for the first year I was living with Belle. During that first year Belle caught on that my son, Gavin, was calling me mommy. Eventually, Belle started calling me Mommy as well. We had a few conversations about it for the first month it happened. I told her she didn't have to call me mommy, she could call my by my first name, I even suggested some nicknames. However she continued to call me mommy.

Now, almost a year later, her bio mom has an issue with it. (Which I understand) However, what I don't understand is what she wants me to do that I haven't already done, because she has been informed of our efforts to let her know she doesn't have to call me mommy. The only thing we haven't tried is punishing Belle for calling me mom. And I refuse to do that because I don't want Belle to feel as though she doesn't deserve my love.

Her mother also has an issue with me giving her hugs goodbye when she comes to pick her up for her weekend. I have no idea what she expects from me. Does she really want me to deny her daughter hugs and kisses when she asks for them yet give them to my son in front of her? I'm so confused as to what my options are.

These issues only came up since we have been going to court. So for a year or so, she said nothing about I being an issue. So after the first couple conversations I stopped telling belle she didn't have to call me mommy. But now that the issue has been brought up, I have this conversation every couple of days, and belle's response is always, I'll call you mother then instead of mommy. I need some advice on how to handle this situation because I'm stumped.