I had this same battle with my Inlaws and to a lesser extent my own mum.
My Mum breeds and owns about 12 dogs, all little dogs but still a pack. Visiting when they are inside when we have the kids is a no no for us, my Mum doesn't like it and I don't care.
My PIL had an older, undesexed male dog who had a very dominant personality, he nipped my nephew on the bum (snuck round behind him and snapped at him) while he was visiting and displayed certain behaviours when our daughter was first born that made me trust him even less than I already did (perked his ears up as if he was looking for a rabbit to chase and kill when she cried etc - as a farm dog it was an activity he enjoyed). My PIL refused to keep him seperate so we just didn't visit.
The day he died was a blessing for us. They have recently got a puppy and we have been really thorough in socialising her with the kids, even bringing her back to our house for a few days at a time so she can be essentially partly raised with the kids and I can trust her with them.
I grew up training dogs and am pretty good at reading body language, I do not in anyway think that a puppy (or any animal) should ever be shoved in the face of a baby BUT I do wonder if the 'snapping' you describe was actually an over excited puppy as it would be very unusual for such a young puppy to be nasty to a person of any age unless there is a history of abuse.
The best way to teach the dog to interact well with your child is to start controlled socialisation right away, such as the pup on a lead when you visit as well as some time apart (crate, outside, other room etc), the worst thing you can do is to actually fully exclude the pup and it will never learn how to behave around you all.