I don't know if these are the right answers or not to your questions but this is what I would do regarding the situations you have described:
Regarding our D14 - since she has verbally expressed that she does not want to talk about this with your H, what I would do if I were him is just write her a short note telling her that he is sorry for the pain he has caused the family, that he knows she doesn't want to talk to him about it, but if she changes her mind then he is there to talk and answer her questions. Keep it simple but leave the door open if she changes her mind.
Regarding the OW - I would not contact her. In reading several other sitch's on this board, it seems like anyone who has done this it has turned out negative for them. Contacting the OW gives her recognition, substance and power. No matter what you say to her or how you say it she will use it against you to drive an even deeper wedge between you and your H.
As for working out with him - if it's something you want to do (work out), I personally would go. You can still be somewhat distant from him in the gym - you don't have to be by his side the entire time - you can be doing your own thing.
Just my two cents - others may have different views for you.
