I'm so the last person to give advice on relationships ...trust me, but I really do feel your pain luvie.
Look - I dont think you can put your foot down here unless you want to nail that coffin lid shut on your engagement. It will look reeaaallly bad if he invites everyone else and not *her* and his boss will probably wonder what is going on too....it just doesnt seem the right environment to do the stand off because he has too much justification behind his motives for inviting her.
What kind of person is she around other people/guys?
See, I'm that flirty type anyways, so girls often think I am *after their men* when I really am not. I'm just being me and sometimes my friendliness is mistaken for interest when its harmless. I'm that icky touchy type and am trying to learn that guys take it the wrong way and girls REALLY take it the wrong way.
When you guys have spoken about this in the past, has it been open/relaxed or the heated type?
Bet you feel like kicking her in the shins when she does the doe-eyed thing whilst you are there, I would
Good luck Jill, you sound like you really love this guy and I wish you all the best
oh and welcome!!