Well ... here are my thoughts. Others will have different responses because they "define" poly differently.
(Not to dredge that up here ... but it is key to why I respond the way I do to this post.)
The thing is, *to me* (all disclaimers about your poly vs. my poly apply) your g/f going to a swingers club (Hedo, I'm presuming) and engaging in casual sex with a man she may or may not see again after she leaves (whether with your permission or not) is not polyamory. It's swinging.
There's nothing wrong with swinging. My boyfriend is a swinger. He enjoys it. I don't. I cannot do casual sex, myself, but I am ok with him swinging for a couple of reasons. One is that he was doing it before I met him and it's part of who he is, so to ask him to quit would be kind of silly on my part. The other is that I know that yes, there is a possibility he would meet someone and develop stronger feelings for them but he doesn't approach swinging the way he approaches a poly relationship (like his one with me). He an I are very much on the same page about the difference between the two with the understanding that if he meets someone while swinging and it looks like it's going to develp into more, we'll discuss it and figure out how to add this person to our relationship, if that's what he and she want.
But .. it sounds like you and your girlfriend haven't necessarily come to an agreement of what poly means to you and how you plan to practice it. The fact that you're afraid that she'll go crazy, disrespect your relationship, sleep around all over the place ... etc., says to me that you and she need a LOT more communication. Being poly is a lot more (again, IMO, the way I practice poly, etc.) than just having sex wtih multiple people. It's about building relationships. And how you build relationships is something you both have to agree on.
Now, that said, if you want make your relationship open to swinging as well as poly, and to individual swinging while she's travelling for work, or similar situations, then that's somethign you'll need to work out in your own mind. But it doesn't sound like you're comfortable with the swinging part of it, to me.
Again, bottom line is that it boils down to communication. I personally would NOT have been comfortable with a new partner who I was still developing a relationship with going off and swinging while being largely out of contact with me.