First question, how long have all of these relationships been? (you+fiance, you+GF, fiance+GF).
You said "triad" so I assume that all three of you are involved with each other - correct me if I am wrong, because that does change the dynamic.)
Do you currently live with your fiance?
Was there ever a time when you all lived in the same place?
How did that go?
How old were the relationships then?
A month-long visit seems like a good "trial run" but being a guest is still a whole lot different then uprooting your life. If she did move there, would the plan be for her to move in with you (or you+fiance if you live together)? Would you be supporting her while she found work? Or would she not move until she had employment set up? Will she have the resources to travel "home" if she feels the need? Could she move back "home" readily if it doesn't work out? What if I doesn't work out with just one of you?
So many details and things to consider...
I don't really know any tricks on the "helping someone not feel homesick" front...(it's something I have never experienced and I don't do serious LDR.)
Me: poly bi female, in an "open-but-not-looking" Vee-plus with -
MrS: hetero polyflexible male, live-in husband (21+ yrs)
Dude: hetero poly male, live-in boyfriend (3+ yrs) and MrS's best friend
Lotus: poly bi female, "it's complicated" relationships with Dude/JaneQ/MrS (1+ years)
TT: poly bi male, married to Lotus, FB with JaneQ
VV and MsJ: bi-women with male primaries, LTR LDR FWBs to JaneQ
My poly blogs here:
The Journey of JaneQSmythe
The Notebook of JaneQSmythe