I suggest that you do a search on here for tags on "jealousy." We have talked about it a lot and it might be very helpful.
Jealousy for me is about un-met needs. I mean the base needs that make us stable humans. Not the need for shelter, food, water... emotional needs. We need to feel loved, cherished, appreciated, close to others who love us and that we love, connection time, quality time with people we love. I would suggest that looking at that might help you figure out what is off balance.
It sounds like fundamentally you are on board with being open in your relationship, which is usually quite different than poly btw... at least by most peoples definition. Although you can identify as you see fit. Poly is about loving another, not going out to have sex with others recreationally. At least for most people it seems this is how the definitions are divided. Perhaps a discussion with your wife about what it is she feels for this guy would be helpful in determining the goal that she has. It might help to see if your goals are still matching up.
If your goals are matching up and she believes herself to be closer to the standard definition of poly then perhaps its time to get more involved with this guy. It makes a world of difference it seems for all parties to be on board and supporting one another. Spending time all three of you together, involving him your lives somewhat, creating opportunities for the two of you to become friendly... all of this helps immensely.
What of the kids? Are you ending up being babysitter while she goes out and has fun? This probably isn't helping you get your needs met. It can build resentment to always be about family time and babysitter while your wife goes out to have a fun romantic time with another... it often doesn't sit well.
Please know that you are not alone. If you read some of my posts from 18 months ago you will see that I was where your wife is now. I understand completely what it is all about and can relate to your situation.... we have worked hard to work it all out and still do. Please realize that it is an on going process and does get easier to navigate with time and experience.... keep at it.