Re: Wife doesn't want to try anymore.
Sorry, my mistake. You mentioned you're uncomfortable with affection like holding hands in public, then you say you have young children. I must have lumped the two together.
Okay, gym guy friend has to go. This you must be firm on 100%! No secret communication, no pass words, no nothing with gym guy. But this means YOU step up. Like wilderness said, (OMG I can't believe I agree with anything he says) join the gym and go with her! That was an excellent idea.
You and your wife have to agree that you work together to fix things, which means no more gym guy, no more secret communication, no passwords, you agree to work out together, spend 2 hours every day alone together, be more affectionate, more loving, get reconnected.
File and move on.
No wish washy I can't decide crap. All in to work it out or start packing stuff. Dude you have to realize you pulled away and so did she.