To me, it sounds as though you feel you really need to talk to each of them more separately before you are ready for an "all together" type of conversation. There are so many relationships involved (even with just three people) and each deserves its own attention.
On the You+G level you have trust/boundary issues that need to be addressed (not using condoms, staying out later than stated, etc.) - this doesn't really have anything to do with H and she doesn't need to be involved in THAT conversation - these are serious issues that he needs to be held accountable for.
On the You+H level - there are actually several relationships: You+H as lovers, you hooked up with her (and her plus another), is this something you are interested in continuing? You+H as friends, which has been absent since she and G got together, is this something you are interested in continuing regardless of her romantic involvement with either you or G? You+H as metamours, sharing the same partner, THIS is the one that might require a "three together" type of conversation.
To me it sounds like she is focusing on the "metamour" level while you feel the at the "friend/lover" level is up in the air. Perhaps you could ask her for a "pre-meeting" get together to discuss your relationship to each other BEFORE the "all-together" get together? This could happen on the same evening if everyone is on board - invite her over, plan on talking to G before she gets there, take a walk with her ALONE when she does, THEN all talk together - everyone in the same place (for support) but having alone time to talk?
Just some thoughts.
PS. I am MUCH more concerned with your issues with G...if these are serious enough I would ignore the H issues entirely...
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