I have a few different thoughts on this:
Me, personally: I actually came to intensely dislike the idea that I had suddenly become a "unit" with my significant other, incapable of leaving the house without his presence, over the course of my last relationship. When I did go to something we'd been invited to by myself, even though it was only interesting to me, I'd get bombarded with questions over where he was and why he wasn't there. When I turned down invitations or had to cancel because of him (he'd have "health problems" at the last minute, which I later realized was a ploy to get to stay home and play video games and drink beer instead of having to get dressed and go out) I'd get asked why I couldn't come by myself, or I'd end up not getting invited to things by those people anymore.
My friends' significant others:
My friend Amy has an amazing, awesome boyfriend. He's great. Any invitation I extend to her automatically includes him, unless I specifically say I just want to spend one on one time with her - my friend group is very non gender-oriented so we don't really do gendered nights out.
My friend Carl is married. We met and are mainly friends through my RPG group. My RPG group is nowhere near as formal as a "club" and it's a very social activity - and I'm presently but have not always been the only female member, so it's not a gender-specific activity.
His wife was originally part of the group, but she ragequit after we switched to a new rule set which she refused to read or follow. She no longer participates, and we no longer play at their house. When we socialize as a group outside of the actual gameplay nights, she gets invited if he is. However, on gameplay nights, we do not invite her. We don't invite the non-participating spouses of the other two married players either, though they are welcome to join the game if they'd like to make a character (one of the wives will join us on rare occasions, the other has no interest.) This applies even though we typically play at one or the other of their homes. Basically, we're getting together to do one particular activity, and it's not a spectator sport.
I do think you should have had a word with Paul a long time ago about Olivia - and he should have been able to make a decision to either continue to be invited to Risk games with the understanding that Olivia would not be tagging along, or that he would no longer be invited if he could not be separated from her presence for a few hours.