I wrestled with the same question, if your spouse's criticism was historically not enough quality time, then is GAL / detach the right thing to do?
The short answer is "yes", and here's why: H is effectively detached himself. He's trying to keep a "safe zone" of emotional space. If you pursue him, you compress his safe zone and he has to retreat to maintain it. If you push him away further by pursuing, you're going to have to regain every inch later.
Here are a few things to consider:
Reading your situation, lack of attention was probably not the only complaint H had about the marriage. You reference the fact that you treated him badly. Do you understand the list of issues that he had with the marriage? Part of DB is understanding that list, coming to terms with whether or not they would be problems for anyone, and deciding to address those things for you. "180's" are practices where when you have an opportunity to exhibit one of those historic bad behaviors, you do the opposite. If you used to complain, you support, if you used to control, you step back, etc. These 180's are far more important than paying attention right now. If you detach but knock your 180's out of the park and are able to effectively GAL, H will come looking for you versus waiting to be pursued.
It also looks like H has been pursuing women outside the marriage since you were dating and throughout your marriage. Is this the same woman, or different women? Why is H doing that? Do you have a theory? If H is a serial cheater, I would guess you've had trust issues, and that may have motivated some of your bad behavior.
One book to read is "The 5 Love Languages" by Chapman. It will help you understand how to make H feel loved, because the way to appeal to H is probably much different than what makes you feel loved. You need to be able to understand the difference and work with it. IMO it's a critical piece of knowledge.
Finally, I think you need to step back and come to terms with your situation. If H says he's done and there is OW involved, there is no quick fix here. Nothing you say or do on any given day is going to have an immediate and measurable effect.
As humans, we like simple cause and effect relationships -- if I do A, I get B. Humans are terrible with long feedback loops and complicated systems, and that's what your relationship is. Therefore you need to work on a lot of things over a long period of time, then you'll start to see results all at once, but it will take much longer than you expect.
As long as OW is involved, you will not be able to draw H closer to you. All you can do is tread water and not make things worse. OW needs to run it's course while you, in the meantime, improve yourself and consequently become a more attractive partner. The better you can do this, the shorter OW's shelf life may be. That said, I challenge you to find a single situation on this board where the LBS was able to say or do anything to get their spouse back once OM/OW was involved. If you look around, the progress never starts until that relationship is over.
H needs to know that (1) you want to save the M, (2) you own the difficulties that you brought to the relationship, and (3) you are committed to becoming a better person for your own good. Once H understands that, your pursuing is done. You can't point out any of your progress, you can't tell him about all the ways that you've changed. You just have to do it and assume he will notice. It's only be repeatedly demonstrating change over and over again that it becomes credible. Talking about it does nothing.
Here's the good news -- OW isn't a real threat. That relationship is based on fantasy. It's not about OW, it's about the issues you had with your M. H's dilemma is not you or OW, it's do I stay or do I go?
You want to demonstrate that you are the kind of wife that only a fool would leave, so "going" would be a really bad decision.
How do you do that?
-- Be responsible for your own happiness -- don't make H think "he's doing this to you and making you feel badly". "Act as If" everything is OK.
-- GAL -- do things that make you a fun and interesting person to be around. The joy you take from your GAL activities makes you interesting and that is infectious
-- 180 -- make H wonder if he really knows the real you. Make him call into question all the assumptions he holds about how you'll react.
I definitely don't think that sitting in separate rooms watching TV is a good place to be right now. You can "give space" while watching TV together if you don't talk about your relationship, your feelings, etc. Keep it light and topical. Alternately, while H is watching TV take the opportunity to go out and do something interesting. Get a life going outside the house. Make H wonder what you're up to.
Good luck RoRoinMD, GAL and detach are definitely the right things to do right now despite H's historic concerns about "not enough attention". More attention right now will sabotage your efforts.
Accuray
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015