I figure if I can get D13 to reconcile with W that our contact will increase and hopefully she will start to notice changes in me.
Okay, listen carefully b/c you are doing what almost every single LBS does at first. You are still wanting to "fix" the stitch. You are trying to control things by forcing your D13 to mend the R with her mom, then mom will be in a better mood to see your changes. That isn't the way it is suppose to be.
If you told your 13 yr old what her mother has been doing with more than one man.....don't you think she needs to be allowed time to process this the best way she can and some space to try and figure out her own feelings about her mother? Now she has to deal with the fact her mom could be suicidal. She has been given too much to deal with. Kids that age ....well, it's hard. I don't think she should be pushed into R with her mother until she's had more time and wants to talk to her mom. If she's pushed into a R, she will only push her anger down within and it will come back out later in a very bad way. Another thing, if your D13 goes too long without wanting to talk to mom, she probably needs some guidance herself.
You need to stop thinking about if your W is going to notice your changes. I can tell you that if that is the case.....your 180's won't last once you've R b/c you were not doing them for you....you were using it as a ploy to get your W back. Make the needed changes for yourself! Let me tell you something.....those 180's are not even attractive to her if you are not doing them for yourself, b/c she'll see right through them. It's all about "attitude". Think about it.
I believe you probably should just go dark and allow her to heal while she is in the hospital. If the doctors think she really is sex addicted, then don't you feel that she needs to attend the session or groups or whatever to get stronger before entering back into a MR with you?
You have stated your concern with her family. That may need to be enough for now. Anymore will be too pushy. Give them space. You can allow phone calls where the children are concerned, but you need to keep the distance. Keep working on your emotional detachment.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!