Hi and welcome, although I bet you wish you wouldn't have to seek advice for this particular situation
Your wife seems like a text-book case of an NRE monster. Now I think would be the time for some serious re-connecting between the two of you, maybe including putting the new man on the back-burner for a while.
Sadly, sex doesn't feel worth it if it's only something your partner does out of a sense of duty to avoid you leaving them. You didn't mention if you are mono heart and soul, or just out of circumstance.
From a very practical POW, would it pay to have the kids in daycare for a while? Is your wife a full-time homemaker or what's eating up her energy? The new relationship? How old are your kids and what do they think of all this? If she's the mother of a newborn this might be more deeply hormone- than poly-related.