Yours is a common story. Husband and wife allow their lives to become so filled up by other commitments, instead of each other, that one (or both) falls out of love with the other. Usually they exist like this for a bit, until someone else comes along. That someone makes time for for the lonely spouse. Makes them feel important, special, attractive. It's at this point that the lonely spouse begins to see what their marriage is lacking- passion, attention, care, conversation....History gets re-written- "I was never in love with my spouse", "I've been unhappy for a long time", "I'm broken inside".....
I'm going to bet that your wife has someone special in her life. It may not be a PA, but it's an EA. It won't take much digging on your part to find out, and I suggest that you do, it will help to know what you're up against. I think that you already realize that with your current schedules your marriage is doomed. The two of you must have lots of alone time together each week in order to maintain a loving marriage. Right now you cannot control your Ws schedule, but you can control yours. I suggest you start finding free time for yourself and your sons, time that you will eventually have to share with your wife if she comes back to you. She must see that there are concrete changes that you are making in order for her to have hope that you can remain a couple.
I would avoid the LRT right now- that's essentially what got you here. You have to be accessible without being clingy and pursuing. She has to be able to see your changes and she won't be able to do that if you go dark. There may be a time to go LRT, but this isn't the time.
