I would like to show her I am hopeful and optimistic about us reconciling. I believe agreeing to carpet and being excited about it would show hope. It would show I do see a future for us without stating it. Actions being louder than words. However, in order to protect myself I would stipulate in mediation that if one of us decided to keep the house they would also take on the any debt accrued for updating the house.
It is only your feelings that wants to tell her, assure her, that you still want to reconcile. They are NOT her feelings! This woman is cold and hard. She does not want you for a H. Reassuring her that you are optimistic, could have very bad results.
When a woman has been in and out of affairs during the M, and treated her H with contempt...........she does want to hear how he still wants to be M to her. Her disdain will rise higher.
You see, telling a "normal" W these feelings, make sense. Your WW is not concerned about losing you! She doesn't care.
You may be able to have a future M with her, but considering her affairs and other behavior, I think she's going to need to experience life without you, first. Don't tell her your feelings. Every time you do, It pushes her further away. She does think like you.
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!