I've read through your thread and I do see hope, but I think your doing some things that are putting pressure on her.
Don't plead or beg for an opportunity to rebuild your R. She already knows what you want and it's not what is important to her right now. I know it sounds unfair and cold, but your pressuring her for a response and that's why she pursues a social life more vigorously. She's running away so she doesn't have to think about it. Her friends offer her carefree fun, play, and acceptance. She doesn't have the burden of a hurting Husband and Kids to worry about when she's with them. She's in me, me, me mode right now.
Why don't you start to look at what you would enjoy doing when she's watching the kids. Don't obsess over her, get a life yourself. I know you said you were not the sociable type, so now is maybe the time to do a 180 in that area. Face and overcome any fears you might have with meeting new people. You might be surprised how much fun and interest you could inject into your own life. Take your focus off your W. Your trying to fix her and your marriage and it doesn't work that way. You have to let this play out on it's own as an observer and that's the hardest part to understand and do. Give up that control.
"It is curious that physical courage should be so common in the world and moral courage so rare." -Mark Twain
