To me, the main thing is to consistently be the best version of yourself that you can be, with her and with your kids.

There are traits in you that attracted her. What are they? Write them down, perhaps even here online. Then aim for developing and displaying those traits every day!

Aim to be the best version of you that you can be.

Are you still snooping? If so, stop that.

Are you still drinking? If so, stop that.

Do you go to AA meetings? If not, my advice is to start going to them now, like yesterday. Go to them frequently and start working the steps.

Continue with your individual counseling, which I assume you are taking seriously.

Continue with marriage counseling if she will still go with you.

It seems to me that living together as if separated is a better option, if you have to choose, since that gives you more of a chance to show her that you are working on being the best version of you that you can be. It will be much easier for her to lower some walls to you while living there than it will be for her to move back in.

Once you start doing good things, keep doing them! Don't give up and definitely don't blame her or get angry or frustrated if she doesn't respond right away. It took years to get to this point, it probably will take a while to convince her that you are in fact changing.