let's start at the end, shall we?

[AnotherStander]

I think I may have lost all hope.

You're barely 2 months since BD and not even 1 since S. You've just begun a long, long journey. It's far too soon to lose hope. If you're expecting to see any changes in your W this quickly then you need to kill those expectations now. This is a journey of a thousand miles and you've just taken a few steps.

W and I had a long talk where I explained how my distancing from her in our past R was a mixed up attempt to get her to show me she loved me

Please read DR and Sandi2's 37 Rules. STOP this damaging behavior ASAP!!! You are doing all the wrong things- you're talking instead of listening, you're cornering your W with relationship talks, you're pushing her into MC. You've got to stop all that and start DB'ing!!

I explained how this kept cycling over and over until I believe she lost the desire to maintain our bond and she let go.

What you need to understand is your W is checked out of the M for now and will be for quite some time. She simply does not care what your feelings are. Don't try to explain anything to her. When you say things like the above it just sounds like you're blaming her. She sees 100% of the problems as YOU right now, and the more you talk like that the more you convince her that she's right.

She had agreed to therapy with me, but I'm staring to wonder if it would just be a waste.

It is absolutely a waste. When one spouse has one or both feet out the door, MC never helps. They just go to check it off their list of "things I tried to save the M but that proved that it was over anyway".

I asked her if she had ever googled the effects of divorce on children, and that was the conversation killer.

(shakes head) Every time you say something like this it's a backslide. It moves you farther from your goal. It sets you back to the starting line.

I really don't think I can live without her, and I know it will kill me to find out she is with someone else. I am feeling so lost and sad today.

YES you CAN live without her. We've all been where you are now, thinking there is no life without our WAS. But there is. As long as you're still clingy/ needy there is no chance she will return. It won't be until you can rise above all that and become the independent, self-sufficient person that you once were that she might look back. So get to work. Get a life. Immerse yourself in DR, become an expert on DB'ing. Figure out your 180's and work, work, work at them. Become the spouse only a fool would leave.

I forgot to add that I know what pushed her away was my shutting down and not giving her the attention she craved, so part of me thinks that my main 180 should be giving her that attention, but with us being separated and her wanting distance, and her not wanting me, I feel like I am in a damned if I do, damned if I don't situation.

You are correct, it's too late for lavishing attention on her. Treat her like a friendly neighbor, but don't go overboard. Just be friendly and cordial.