Wife seems open but it feels like our relationship is broken. Help?

My wife has brought up before, “maybe we should have sex with other people.” For a while like over a year she has been calling Will her boyfriend. It’s usually in a playful way as we both have kids the same age and sometimes Will and my wife end up taking the kids to do something. This is all good and fine. Except when I feel it becomes unhealthy is that to other people and publicly my wife calls him her boyfriend. Which I’ve generally been able to laugh at. Except when in front of my brother she was talking about her “boyfriend Will”. Which was obviously very awkward for me and my brother. But also among friends she’s talked about how hot Will is hot, etc. during a fight the other day I finally snapped and said she can just go hang out with Will.
Fast forward to July 4. We are hanging out with another couple we are very good friends with. My wife brings up the fact that “my husband thinks I have a thing for Will.” Then she says that “she thinks Will and his wife have a thing for us” (meaning swinging). Our friend asks if she would like that. To which her response was “ I would be into it but guess who wouldn’t “. Then my friend says “so you want to get railed by Will” My wife doesn’t respond for a few seconds like she’s thinking about it. Then says “I think I would be more into his wife”. I stay silent this whole time. No one asks me anything. I let it go but later she can tell I’m distant and a little upset.

Tl;dr

The whole conversation confirms my thoughts and feelings. She denies to have a thing for Will in front of me but the opposite in front of others.

Mind you we have kids, a sexless relationship, she is often mean and controlling. She suffers from extreme anxiety which is the root of most of our problems. And she blames my reaction to her anxiety as her biggest concern.

How do I move forward?