If her reasons to want to split are that I wasn't there for her and the kids through depression than my 180s have to be the opposite of that.
So how do I detach yet still do 180s to show that they are my priority? I can't just disappear: that's why she wants the divorce. Because she felt abandoned.
I think in your case you can tell her that you understand that she wants a divorce however you are not giving up your kids and you are going to do everything possible to be the BEST DAD you can possibly be. And PROVE it by actions not words.
You are sorry that you were not there for her and your kids however you do not want to let that continue into the future. If she wants a divorce then that is fine however that will not stop your determination at being a great DAD.