so now that I've received a good cross-section of responses I'll tell you all how I feel about this.
as I'm quickly finding with most things baby-related, I actually feel both ways about it. completely on the fence (which is unusual for me as I'm usually much more one way or another).
my mil is quite needy/clingy, still refers to her boys by their childhood nicknames despite them both complaining about it, calls these grown men "my babies" so honestly i'm not in the slightest bit surprised she'd continue on in this fashion. in fact I expected it.
fil is the complete opposite and dh doesn't see him hardly (mil and fil are divorced obviously) we didn't even get a card after ds was born. so, when you have such polar opposites for in laws, you do appreciate the more doting party as it means they actually care. so in that respect I do think it's lovely as its part of the whole affection package that someone cares about their adorable little grandson. also, on a logical level, I know there's no malice intended. she's not saying "my" to belittle or trivialize my position as his mother.
there is a tiny part of my ancient mammalian brain however that makes me roll my eyes. I think this is more a reaction to mil's general clingyness rather than simply referring to ds as "my", which I agree would be pretty petty.
so yeah, completely on the fence with this one. and I don't intend to do anything about it, as I don't believe you really can. you just let it go and roll your eyes in private but appreciate the fact my baby has such a loving grandparent.
and yes LLH I completely agree with what you said too. if it's said with bad intention behind it (ie to undermine the mum) then I agree it's awful.