I am a mother damn it!

So a little back story. AND THIS MAY GET LONG. I married a man with a crazy ass ex girlfriend (yes girlfriend) and a beautiful barely one year old baby boy. I emphasize girlfriend simply because he had no intentions of being with her but she got pregnant within 6 months of "seeing each other". He tried to make it work for the sake of his son and of course it didn't work. Like i said in the beginning she is crazy. They knew things couldn't work but had just signed a lease so he did his own thing and she did hers. That's when we met and she met many men during this time. She was a SAHM so he paid EVERTHING, 3k a month. He moved in with me and she stayed at the house. Once she got a job he was with the baby when she was at work and vice versa. Well months went by no problem but as soon as she found out exactly who I was she lost it. She had known he was with someone hell they hadn't be in a relationship in months when I met him yet she went bat shit. She called the cops, lied and had him arrested for domestic assault when he's never touched her. She has actually hit him and left bruises and he never did anything because he knew she would take his son and children born out of wedlock in TN the fathers have no rights until taken to court. Of course we had the charges completely dropped after her keeping the child from him for over 2 months and the judge read all the texts from her begging him to come back and that she would admit she lied LOL I know. Fast forward to now. My husband refuses to talk to her. And I don't blame him. She has stalked me, shown up at my works and called me NUMEROUS times under restricted, comes by our home and literally bashed my name to everyone calling me a whore and home wrecker although she was sleeping around the whole time. My only concern is the child. That's all. I don't care what she says or does but what really pisses me off is what she continues to text me saying. The child is now 3 and he calls me mom or Courtney. Mainly mom. We have NEVER told him to call me that but his bio mom is NEVEr around him. She puts her with a baby sitter from 9 am to 7-8 pm on a daily unless we have him which is 50-50. We correct him and say no Courtney but he says no your mom. She recently texted me saying I'm not a mom simply because I didn't birth him lol I seriously pity any woman or mother who thinks this way. I have spent my last dime and all my savings on this child. She cost us everything because of the false domestic assault claim and custody. 15k for lawyers and restitution. Not to mention she gets my income tax bc she took him to court for back child support from when she was living with him lol if you genuinely believe that "step" moms like me are not mothers I feel sorry for you. I take care of him everyday we have him because husband travels for work and is wore out. I do everything for him and he recognizes that. He decided to call me mom because he sees me as his mother. If you think women aren't moms because they didn't birth a child please go tell a woman who suffers from infertility and adopts that they aren't a mother or a parent. Tell a woman who has had a still birth or miscarriage that they aren't a mother. I carried a baby inside of me and lost my baby before I went to term. My child isn't here with me. I am no less of a mother then you. Quit being so ignorant "bio moms" time to grow up.