Just caught up with this thread. As others state, you are doing really well MLMM. You are receiving excellent advice. Just a few thoughts.
Trying to nice her back was pretty much doomed to failure but I can understand why you did it. I think three things occur when the BS tries this without actually showing strength (I'm not saying you didn't have it but you failed to show it at that stage) and confronting the WS directly:
1. The WS is still in the so-called fog of selfishness and denial and wants to continue with the illicit thrill of sex outside marriage. Therefore, any attempt by the BS to win them back is not wanted.
2. In fact the WS somehow loses respect for the BS. They just see the BS as weak in comparison with the OM predator.
3. Counter intuitively, it strengthens their resolve to continue with the affair. They have the perfect cake-eater scenario. A supportive, loving husband to provide long-term security and a young vibrant lover who panders to their need for validation and sexual thrills.
This is why your 'pick-me' dance never had a chance. If anything it made things worse.
If your wife starts to show true remorse and you anticipate the possibility of some sort of reconciliation after the divorce, please do not rug-sweep the affair. If you do then this will prevent you healing. She needs to give you a full time-line and you need to discuss both the issues of the affair and then at some point the issues of the marriage. She certainly needs IC to get to the bottom of her brokenness.
A good marriage needs love and respect. Affairs can happen even in a good marriage, often because the wayward is broken in some way. So affairs can happen even when the WS still loves the BS. It rarely happens though when the WS has respect for the BS. However, that is not the full story. It seems to me that the main cause of the WS losing respect for the BS is that they have lost respect for themselves. They then seek validation outside the marriage to get this and in order to justify this to themselves, they find something to latch onto to 'lose' respect for their BS, in most cases with little or no justification.
So, it may be that you were in a good marriage and your wife actually both loved and respected you but because of her brokenness was able to create a scenario in her own mind to justify the affair to herself.
Now, of course, she is devastated as she never wanted to lose the marriage, you and her family. She just wanted validation, some illicit thrills and sexual gratification with no consequences. You did nothing wrong and she knows that but you have shown your strength and given her consequences and she is floundering.
She now seems to have seen the light. She may eventually become truly remorseful and be a possible candidate for reconciliation if you offer her that gift.
You are in the perfect position because of your actions to offer her that gift from a position of strength, whilst retaining your self respect. So well done.
It may well be though that after the divorce you want to move on, that is your right too.
In either event, please remember to maintain the high moral centre and treat your now hopefully remorseful wife/ex wife and the mother of your children kindly and with the respect she should have shown you, as that is the right thing to do.