The "not had an identity" statement is typical of MLC. My husband said the same thing during his (almost the same words!!!).
Yes, sometimes OW is in the picture longer than we realize. That's NOT saying your OW is still in the picture, but they do add to the confusion of an MLC husband. Please try not to take OW and their realationship personally. Your husband's relationship with her is completely about himself. It's not about her. Everything I read in your sitch indicates MLC to me and she just happens to be convenient during a time of confusion. He's just trying to grasp for the happiness straw and hasn't yet embraced the fact that it's right in front of him (his wife and family).
Why do you want your husband so bad? You want your family together, you are not a quitter, you are smart and sensitive enough to realize this isn't about you or your marriage, it's a stage in life he's going through and you've decided to hang in regardless of where it goes... and you're willing to go "down with the ship"... and will have no regrets even if it does sink because you'll know you did your best to keep your family together, and you'll be a stronger and healthier person in the long run. Also, the weak break apart, give up quickly and run... you aren't weak.
There is no arriving, ever. It is all a continual becoming.
