To the person who asked the second question:
Quite obviously, your wife is swinging and you are poly. The two are pretty different and can't be expected to work the same way. Poly without love is like swinging without sex, but just because she is swinging doesn't mean she understands how poly works.
Your wife seems that to have problems with you being emotional with someone else. It's not unusual, studies shows that men tend to have more problem with women having sex outside the relationship rather than being in love, while on the other hand women struggle more with the emotional aspects than the sexual ones. Not saying everyone works this way of course, but it seems to be the average. So you need to understand this isn't a double standard on her part. She wants your poly to be like her swinging (hidden, in a specific context, over when a session is done, with no attachment, with several people...) I don't know exactly the details of her swinging but it seems obvious she expects you to follow similar rules.
But you're not swinging. You're in a polyamorous relationship. And what defines polyamory is the love. A relationship can be poly and have no sex involved, but without feelings it's not poly.
But sex is an act, with a beginning and an end, while love is a feeling and it stays there. So while you're with your wife, you still love your girlfriend (an vice-versa) while when she's with you she's not having sex with her playmates.
If she wants to be completely out of your polyamory, or rather, for your polyamory to be disassociated with her, she should know it's not possible. Even if you decide to work on a primary/secondary model, where you have different "ranks" of partners and she'd be a primary one, all your partners are part of your life.
However, that doesn't mean you can neglect her, either, especially if you're under the influence of girlfriend-induced NRE.
Talk with her about how she feels and what causes her to feel that way. You can create boundaries, yes, you probably should have already, but be careful that these boundaries aren't just hiding the issues away.
I agree that you can try seeing each other away from her if that helps her, for now at least. That would make things trickier if you plan to move in together later on though, so it's more likely to be a temporary solution, especially if you don't want to end up with some kind of double life. I mean, most of my best time is spent with several partners at once, and it would be hard having to pretend like one of them isn't my partner.
But you probably have a lot invested with your wife, so the advice I would usually give (leave anyone who can't live with your being poly, as the relationship would be painful for all partners involved) has to go on the back burner here, and I would suggest you try to work things out with her and go slowly about things. The advice often is to go at the pace of the person who struggles the most (and that seems to be her, here).
Go ask on poly forums, too. A lot of people there have experience with mono/poly relationships. And she might be non-monogamous too, but she still seems monoamorous, so they should be able to help because they've been there or they've seen it before. If she is mono, every affection you have for your girlfriend might feel like less affection left for her. I'm poly too, I know that falling in love again makes me more in love with my current partners, not less, but to a mono person it seems counterintuitive because that's not how they work at all.
The bottom line is, poly has structures and rules that are common to the community, but with poly, you kind of need to find the rules for each relationship individually, and you might have neglected that step. And you need to constantly check that everyone is fine and everything is okay. It's demanding of course, the more relationships, the more work, but it's rewarding too, and when you're in love you want to make it work.
Good luck with everything. I know it's hard being the hinge when drama hits because you feel like every decision you make might end up hurting or disrespecting one (or more) of the people you love, but in the end, I've always been able to find the solution that was best for everyone, and I'm sure you can do that too.