The problem with asking for other's opinions on matters like this is that it's so centred around each person's own experience and feelings on the subject that you will end up going out the same door you came in - not really much wiser!
And, of course, none of us quite know the dynamics of the OP's family relationships, nor their history. Some small event, incident, seemingly unimportant and not even mentioned, can alter the whole picture.
If my son had spoken those words to me, I'd have been a tad shocked and upset - but that's because he was quite laid-back about becoming a father for the first time and because we also have a fairly relaxed and informal relationship with each other. But, we're all different and have a variety of family set-ups, so my situation is irrelevant really.
I hope the OP can just 'go with the flow' and accept that parenthood grabs people in different ways... it's early days yet. Best perhaps to just follow the 'rules' and be as helpful as possible, knowing that you are doing the right thing... but subtly make sure the parents understand that you are a blood relative and not the hired-help, and expect a small nod of understanding in that direction.
A quote for those blessed with a spouse:
I hope the new PM is kind to Larry the Cat


