Feeling ever so slightly miffed

Oops “there” not “their”

If this +1 is their SO then they should have been invited, if not, then no invitation means no attendance.
From your point of view numbers may be critical and if their is an element of “formality” then it May not be easy to add another guest.
You don’t say who the guest is or who the +1 is, if you were to it might make things clearer. Bottom line is that even if they did not ask you are within your rights to say No.

I'd go with the flow. Dh and I love talking about 'funny' relatives. It's the stuff of family life.

I would be miffed too. Is this ‘third party’ a Significant Other or a relative who can’t be left alone? Otherwise I would ask your OH to see if this uninvited extra could be uninvited.

Oh dear, an unfortunate start! Yes, they should have asked first obviously. I can imagine how galling, but perhaps to avoid things getting off on totally the wrong foot, just swallow hard and make the best of it?
I can’t understand how some people are so thick skinned and oblivious of how to behave.

Ah the vagaries of families - use this experience as part of getting to know them. Then you'll know what to expect when next you issue invitations out and can then either invite, or not.