Oh wow how annoying! 
I do feel your pain @blahblahdeblah I had several older family members giving advice, and telling me what I was doing 'wrong' when mine were little, as if I was too young, too green, and too stupid to know how to look after my owns kids. I was older than ALL of them when they had THEIR kids too.
And they always spoke to DC.
'Ohhhhh, no coat?! Your mommy is naughty isn't she, not dressing you right'
'dear me, a bag of maltesers, your mommy should be giving you an orange, naughty mommy.'
'Aw you look so sad - has mommy not changed your nappy? Naughty mommy!'
I am really pissed off with your partner for LOLing at it. What a twat. I would be tempted to bloody move out, and not tell any of the fuckers where I live!
No advice really except to say (firmly) that your DD is absolutely FINE, and tell your partner that she'll be BANNED from coming if she doesn't quit!
I am sick of it being accepted for people who are a generation (or two) older, being allowed to say whatever rude and obnoxious shit they like, and people not calling them out, because they're a 'senior.' It's not OK. It's really not. I can't imagine saying rude shit to people like this. Why the hell do they say it? 
I can only imagine they have always been rude and obnoxious as there is no WAY I would talk to people like this, and I know several people (over 65) who are really lovely and supportive, and would never say anything negative or critical. So not every 'senior age' person is rude, but when they are, they don't get 'called out...' 