For what it's worth, here's my two cents:
First, you really haven't given much background, so my advice may be totally off...but, here's what I'm seeing.
Your husband is away often and for a long period of time, so you both agree it's okay for you to get your needs met elsewhere. He's allowed to play with whoever it is you find, as well, when he's home. You find a couple...your husband meets them once (?). Maybe more often....but I'm guessing with him being in the military, that's unlikely.
I'm not faulting you, but you DID have the ability to choose whoever you wanted....and you chose a couple. I don't know Hanna's situation, but she doesn't really OWE you and him any alone time. Maybe her expectation was, "Oh, this other woman is lonely. I like her/am curious about exploring with a woman/whatever. Sure, she can spend time with us." She may see your requests for alone time as forced attempts to shove her out of the picture (even for just a night), and she may well resent that (wouldn't you, in her place?). ESPECIALLLY if you didn't agree on you and him being alone beforehand. Also, it's not her fault you married a military man that's gone a lot. She may have no interest in finding another partner away from him.
It looks like limited, shared time with her is all you're going to get with him. So, you're probably best off either finding a new couple, whose expectations better fit in with what you want....or sharing another partner (like you are now with Hanna)....or finding a guy who can spend a significant amount of alone time with you, without expecting you to be his one and only.
Not saying it'll be easy, but it might help you be less lonely.