I've not read all the posts, but have read all of the OP's.
I think, the OP's partner is using the situation with his children to remove himself from his partner's issues.
The partner is being a 'Disney' dad. Just having the good times with his children and not want to deal with the discipline issues, setting boundaries etc.
He is also doing the same with the OP. Just dealing with going to work and not actively supporting his partner assisting with parenting her children and, more importantly, being a supportive husband, helping with her emotional needs.
He is escaping from all joint responsibility every single weekend. How is that being a partner?
Of course he should see his own children. But he needs to incorporate everything together.
Also, if the OP is the main earner in the family, who is paying for hotels every single weekend.
I think OP is being taken for a mug by her partner, in the guise of needing to be there for his own children.
I think it's time for the OP to cut her losses and for the partner to leave. It may be difficult at first, but at least her life would then become more regulated on her terms and not on his and his children. Hopefully, her mental state will improve as well with lots of therapy and a more relaxed stable home life for her and her children.