Abusive new partner

My oh has a son at 2 his mom got a new partner and has changed his weekend to every other weekend and one day a week. My partner took her to mediation to get on the birth certificate and she's refusing and has made up she has safety concerns (he doesn't have his own room, which he does! My partner doesn't use reins when taking him to the shop right beside our house, no roads etc) we have just found out her new partner isn't allowed contact with his daughter due to domestic violence and has to see her in a contact centre. She also has rang mediation because my partner wouldn't video call her because we had family over seeing little man! But she's broken 2 of the conditions set by mediation, comes earlier to collect him while he's eating, drops things to our house and demands to see him while he's at his lunch! Should my partner mention her partner while in mediation? He doesn't want him around him as he's came back to us with a burn on his ear which she blamed us for but weveproof it didn't happen here.

And what is some other things that should be addressed while there?