I try to picture it this way.
There's a circle that is the relationship between you/him.
Another circle is the relationship between him/wife.
Another is him/child.
Another is wife/child.
THEN picture square for responsibility (or use a different color circle).
There's his to child (parenting)
hers to child (parenting)
THEIRS as co-parents to each other (parenting)
Theirs as roommates (bills/home maintenance, pets etc)
That's just from what I read in your post. I have no doubt there are more.
Anywhere that you are crossing into one of her circles or her squares-he is not at liberty to make choices alone.
It isn't that he has NO SAY SO. But that he has no more say so than she does.
If that makes sense.
Much like 50/50 business partners.
(the last page-last few posts in that other thread-are directly addressing issues that have arisen with metamours in contact with children. Might give you some more info to consider)
"Love As Thou Wilt"