I am sorry you lost your baby. For his mum to even say such a thing is terrible. Your MIL sounds a lot like mine. My MIL lost a daughter before my ex was born and when she had him she focused all on him, to the point of family division, anyhow she wanted to be #! in our marriage, I fought her tooth and nail for 11 years. At our wedding she didn't not smile, not once. She made my life HELL. When we had kids I was afraid she would try to "take over" When they were born she tried to at first but I put a stop to it right off. She was mad because of religious differences and would tell me my children were going to hell. But was sweet as apple pie when my ex was there. She used guilt to make sure that birthday parties family get to gatherings all revolved around her. She actually scheduled a birthday party for her husband on Mother's Day one year so that I had to chose where to be. I was not at the birthday party. She HATED me from day one. I am sure she threw a party when I left her son. LOL
Get out while you can. It will not change. I am sorry for your loss but be glad that you will not have to fight this woman over and over again for the right to be a mother to your own child.