In your situation, I would try to get an older puppy, or a retired show dog, that has some training. It's not fair to leave a growing puppy routinely for 8-9 hours at a time, it's Ok occasionally for an adult dog, but not during the critical growth, training and bonding period of a puppy for the first year or two. You could get a pet sitter or trusted neighbor to let the puppy/dog out etc... If you could time a puppy coming home when your wife is out for the summer, (probably too late for this season) it could work to get a puppy, because by the time it is time to go back to school, they puppy should be crate trained and housebroken, if your family works hard, but still too much for your parents to take on for a while.
A Labrador puppy will not be "gentle and undemanding" for your parents for at least a year or two, and will need to be taught to be gentle with the Yorkshire Terrier. Labrador puppies are rambunctious, and don't know they are bigger than their smaller playmates, and can accidentally hurt them.
Puppies, especially Labrador puppies require a huge time commitment at first, to have the time, training and patience to become and well behaved member of the family. Labradors are Great family dogs, but they do not come straight out the chute that way.
So my advice would be to call around and see if any breeders near you have an adult they want to retire, that is already good with kids and small dogs. In this case I would not go the "rescue" route, because you have kids, elderly family members, and small dogs in the family, a well socialized show or competition dog that has good manners and reliable background would suit you really well I think.