There's a bit of this going on in my family, too... My DC are both double-barrelled, but one uses both parts, and the other uses only the first part. Entirely their choice - I figure that their names are theirs to do with/use how they like. I also only use the first part of the surname... having legally changed it from my father's surname as soon as I was old enough to do so (for no reason other than I hated the name and always had done, and my DF was lovely about it). My children's name also uses my father's surname, though, because he was quite upset when my oldest was born about his name disappearing completely. It was a small thing, it made him happy, and I figured that my children might like his surname even though I don't (one does; one doesn't).
Neither have their fathers surname.
My maternal grandmother persists in sending us mail address to "Miss My Father's Surname", for me (I'm neither "Miss", nor "My Father's Surname" and haven't been for 25 years now), and "Miss/Master Their Fathers Surname" for the children. For a long while I'd patiently correct her... think it was all sorted... then find myself gritting my teeth the next time she sent cards. It was a total faff, because she'd send cheques for birthdays, the children's of which I'd then have to sort out (never cashed mine: I have never wanted anything from her; but the children's weren't mine to decide about, in one way). An endless loop of frustration and irritation. And then it dawned on me that she wasn't doing it because she was forgetful - quite the opposite. It put her in the position of being a victim, of some sort, whilst she was manipulating my emotions and controlling a situation. I stopped correcting her. I stopped contacting her about changing the children's cheques over (I simply gave them the amount myself). She contacted my mother (whom I'd not lived with for over 15 years at that point) to ask why. Not me; my mother. As though I was nothing more than a silly little child who needed to be put back into place by my elders and supposedly betters. My mother asked me, only to be told that I'd made the executive decision that if my grandmother couldn't have the manners to respect mine and my children's names - then I wasn't going to respect her need to be in absolute control of us. We'd never been close (for various reasons, which I won't go into here), my DC barely knew her, it wasn't a hardship not to have her in our lives (in almost 12 years, she's met my DS three times - upset him to the point of tears twice, and told him that Santa doesn't exist, on Christmas Day, when he was 3 years old!).
Now, she tries to send the cards through my mother - who realised that she couldn't force me to accept them. After all... they're not addressed to us, they're addressed to people who either have never, or no longer exist...
As for my ex-inlaws, they were quicker to grasp that the DC don't have their surname at all. They knew me when I still had to use my father's surname, so it took them a while to grasp that I'd changed my name (my own parents took to the change very smoothly, in comparison) and the concept of the DC not being labelled as part of "their tribe"... confused them, I think, into simply not bothering with surnames. Any/all post is addressed to us by our first names. Much simpler.