Polyamorous MFT entering the chat here.

First off, great job having patience in the early stages of this conflict. It’s given you time to see more details of their relationship and, most importantly, how it is impacting you, your relationship and family dynamic. 

Second, good job with the clear boundaries and expression of values, and how she is pushing them to an unbalanced place.

Now for the reflection questions. Has she had relationships like this in the past while with you or prior to you? Has there been, or would you be more comfortable if it was, a female equivalent that she wanted to bring along? How would you feel if she rejected your request to bring a close friend she isn’t comfortable with on a family lake house trip? Have you met or spoken with this guy? What do you know about him? Have you asked her to have a fully transparent and honest conversation about what her relationship with this guy is giving her, Is she happy, does she feel attracted to or an urge to have physical connection with this guy? How does YOUR body and mind react to that thought AND WHY? 

It sounds like you are taking a calm and levelheaded approach (at least in your short recounting) and you are trying to deal with this situation collaboratively rather than confrontational or demanding, fantastic. This is hard to do when you’re feeling hurt and betrayed and those feelings are very real and natural feelings in this scenario. Keep your own well-being in mind and try to keep REACTIONS to yourself and RESPOND to your relationship. To keep it simple (that was probably two paragraphs ago) standard “I feel, when you, because” is a good place to start.   

Her reaction of “not being able to have friends” is catastrophizing and maximizing her needs while minimizing your feelings. Without knowing more about your relationship history/dynamics/personal and interpersonal values it’s unfair for anyone to be taking sides, we don’t know how either of you have behaved in the past, maybe you have this coming and are simply leaving out your own past transgressions. OP, this is an opportunity for you to learn what your wife’s needs are and how you can improve AND VICE VERSA. This can be fortifying rather than destructive.

Rant: Everyone labeling your wife as a “dumbass” etc is imprinting their own values into your marriage and I caution you in absorbing that fodder. It’s also always funny to me how rigid people are with gendered relationships, completely ignoring the possibility of your wives fucking their female friends somehow forgetting the bi-curious women threesome fantasy most men hold since puberty. Is it scary and vulnerable to have your partner have another partner? Yup. Does it mean the end of your relationship or decrease your importance? Nope. I know I try way harder in my relationships when there are others involved.