However, the answer is more complicated than that.
Dogs live in packs, you are (or should be) the pack leader, any other member of the family comes next and last is the dog. if you have multiple dogs, they'll decide for themselves who is more or less dominant.
A new born baby is a new member of the pack, generally starting at the bottom of the pack.
Here's what you need to do: Use as many tricks to make the newborn baby higher up the ladder in the pack. Examples are taking away the food with the baby's hands while the dog is eating, making the dogs move for the baby instead of vice versa, etc ...
If your baby is more dominant than your dog (in the world of the dogs) you will not have problems with the diapers (nor with agressive behaviour when the baby goes first, takes food, etc).
Cats on the other hand are no pack animals. If your cat decides your baby is a threat to their territory they could start spraying everywhere.
To try and fix it is simply correcting your cat on the spot (water is very efficient, spray some when you see your cat urinating in-house).