Also who ever said he is testing your boundaries with regards to the children meeting OW is spot on.
He didn't ask 'can OW meet them now'.
He said he, OW & kiddies were invited to something to see how you felt about it. Then when you got upset (not surprising) came the not my fault, I didn't invite us & them.
Pure deceitful manipulation.
Being me I would be tempted to text (so you have proof) him and say you have thought about it and the children SHOULD go with him & OW to the party (dependent on them wanting to of course but don't tell him this).
See what he does then. If he says yes it will be bloody heartbreakingly hard for you but you will know exactly where you are with him wanting/not wanting OW to meet them. Which will say a lot about his real relationship with her. Not that a no from him actually would mean they are not really happy.
He didn't say anything about being unhappy with you but went off.
He is saying lots about not being sure about OW but he is still there. In her bed every night. If he was unhappy/not sure why would he stay there?
He was happy enough to dump you as soon as he could.
His actions are a lot more clear than what he is saying.