No Contact while co-parenting, and dealing w/ his crazy new fwb

How do I go about No Contact effectively when I share custody of our child and have to co-parent with my ex?

My ex is in a “fwb” relationship with a woman with three kids going through a very volatile divorce. She’s very needy and manipulative and enjoys throwing drama my way every chance she gets. This has also been difficult because I do let her get to me. It kills me as I have no clue what he sees in her. She’s an alcoholic, has only been seperated from her husband a few months, went back to him once, has three children to whom she’s a terrible mother, she’s clingy and needy, as well as emotionally manipulative, and not to be superficial and judgemental but as far as her outward appearance she is overweight, a bit dumpy, and not particularly attractive. She’s also nine years older than my ex, approaching 40.
My ex says he hasn’t moved on yet he spends an inordinate time with her. If he does move on this is the last woman I’d want in my child’s life.
Do I just ignore it when she tries to cause trouble?