There are three things.
If she's spoken to a mediatior (if) she could have changed her mind as she didn't hear what she wanted, she could to the MIAM and mediator doesn't believe mediation is appropriate and sign off straight to court, or can go ahead the mediator would be the one to contact ex.
But, if this is going round in circles why doesn't BF go to a mediatior and invite her?
Stop her being in control and face it? By taking some control, the stress will come down as he won't feel so in limbo.
He gets to decide who looks after children in his care, irregardless of ex's wishes, irregardless of a cao or not. Can you not look after the kids while he has his weekend away? If he's that bad and needs the break I'd offer at least and mean it (unless you're away too).
I think both would benefit from a mediator and agree a parenting (co-parenting) plan and for his ex to hear some truths from a mediator that he can use as boundaries for himself with her at the very least.
Separation is so stressful, emotional, exhausting for all involved. Sorry he's struggling. I'm sure she is too and none of this is ultimately helping the children. Sounds like he's involved which is a great thing.
We parents don't usually get breaks! I did a full time job, parented and divorce so 3 FT jobs it's was so so hard and I definitely had wobbles but it's better the other side with things settled and clarity. The nonsense doesn't stop, but it does rachet down with time. I things get easier with time.