My parents, occasionally (my Dad really) and more so my in laws (MIL especially) seem to take my requests re: my kids when in their care as a personal insult. They get all huffy and accuse me of being paranoid eg when I run through a checklist etc or ask them if they're 100% sure how to safely buckle the kids into their car seats etc. But MIL shows she doesn't know everything all too often - putting 2 week old down in Moses basket on his side, not feet to foot etc. I was there a minute after and corrected him but her body language gets all defensive when she sees that. With my older son she bundled him up in 3 blankets and a hat indoors while he was a tiny and she watched him for an hour or so one evening so that DH and I could go for a little stroll.
If I raise these things with DH he gets all defensive and implies that if I trust my parents then why not his mum (who he feels is more capable and switched on etc). The difference is that I can much more easily tell my parents how it is and what they're doing wrong without fear of offending or making things awkward. MIL is quite arrogant (years as a single parent of 3 necessitating self-sufficiency and self-assurance) when it comes to childcare and it annoys me, kind as she is in general. How do you handle these situations?