Your very own words:
"Looking back, I could have done better as a husband".
"Apparently the gaming was a little too much (looking back, it was)"
"My dumb self said 'then I guess divorce is next'"
"Looking back, I lacked interest in her and I recognized that"

Now, SHE is the one being ridiculous?! Wow. If your intention is "I'm sort of using counseling as that session in which it may help her realize how ridiculous she is being" then it is better off if you divorced, as was YOUR suggestion in the first place.

What happened to owning your part in it? Of how you were not the best husband, not always there etc. when your wife was carrying your child and struggling with post-partum depression.

Now the narrative has changed - SHE is the one who is demonised and being "ridiculous"?!

At least, whatever you do and whatever issues you have with your wife, please don't drag an innocent child through a rough (contested) divorce. There is no need to traumatise that little girl because of whatever recriminations you now hold against the mother of your child.