Need advice about people around my baby

I have no issue with the father of my child. The issue is his girlfriend. She has anxiety and depression and in the last 2 months has walked out twice for 2 weeks and caused constant arguments with my ex. I'm concerned to have her around my baby when he's in his dad's care. Can I stop her from seeing him as I'm afraid she will kick off or have a moment in the home when my son is there. His dad had agreed to have his unsupervised access away from her but has now been told that she should be there with him but I'm worried for my sons safety and don't want him around the tension and arguments. Can I stop her seeing him? What can I do

He agreed with me that it would just be him and his son during the unsupervised visitations but has spent them with me. I told him to go off on his own with his son to bond but he wouldn't. It's like he's scared to be alone with the child. He says he ensures that his home is a safe environment regardless of her being there or not but then agrees with me that she shouldn't be around her. I don't know if he's trying to keep her happy due to her issues but it's now compromising his relationship with his son.

Baby is 6 months this month. He doesn't have any family down here. They all live up country so there's noone available to be with him.