This is from Miss Manners. The question just cracked me up....
D EAR MISS MANNERS: A rather despicable married friend has been estranged from her husband for years, yet they maintain a home together. She has had several love interests in the past few years. I suspect I’ve been used as her “beard” for some of her escapades.
I don’t really wish for her to be at our wedding, but nonetheless must invite her. I despise her husband and he feels the same of me. Is it permissible to simply invite her? I know her husband will not attend, and I fear if I address the invitation to Mr. and Mrs. it will encourage her to bring a guest.
If I’ve painted a portrait of a woman who lives beyond the conventions of etiquette, I have painted well, so please don’t say she’ll have sense enough not bring a guest other than her husband. She will not, and I can’t abide the thought of a married woman bringing a date to our wedding.
GENTLE READER: Are you seriously sticking Miss Manners with the premise that this person is your friend and you must invite her?
All right, but then she also accepts your premise that your friend is beyond the conventions of etiquette. In that case, if she wants to bring a guest, she will bring one, regardless of what you put on the invitation.
So you might as well do the correct thing and invite the couple as a couple. If a couple maintain a home together, etiquette does not investigate whether they are getting along.
I'm gonna go with 'not my circus, not my monkeys.'