Dog trainer/behaviour consultant here..
Your parents are being very stupid, and they don't appear to understand the first thing about introducing babies/children and dogs, nor do they seem to understand dog behaviour.
So for those reasons alone I would not entertain them having the opportunity to introduce your baby to their dog.
Yes, it is unfair to simply shut a dog away when there are visitors and the dog is not used to being shut away - so it is their responsibility to ensure their dog CAN handle this and is used to it, by... training their dog.
When 'introducing' dogs to babies/very young children... actually what should be done is not 'introducing' at all - owners/parents should work hard on rewarding the dog for looking and NOT approaching, for moving AWAY from the child, and for ignoring the child and seeking out an adult.
Teaching dogs to approach children (and vice versa) is at best silly and at worst really dangerous, we do not want dogs thinking 'yes I should definitely ram my nose in this childs face/climb on them/they are a source of treats/they taste delicious due to all the stickiness'...
The ideal goal for a dog around little kids is to think 'I should go away over here and ignore that, I should listen to the adult people, it is rewarding to avoid that baby and nice things happen when I do'.
Unfortunately SO many people want to shove the dog in the babies face, teach the dog to approach the baby or teach the child to toddle up to the dog or crawl up to it, teach the child to pet (ie, hit, slap and grab) the dog... in many cases people actually PUNISH the dog for trying to move away from the baby or trying to communicate their discomfort by freezing/lip curling/etc. All of this stupidity adds up to bite incidents!