This is unfair to the pet. Parents also think that the pet and children will entertain each other. Young children usually quickly lose interest in the pet and dogs especially need mature interaction that only adults can give. Caring for an animal is a 10 -15 year commitment. Remind prospects they may have to board animals during vacations and must plan for their needs before contemplating a move.
Relocation is probably the number one reason that dogs are abandoned.
Get 2 personal references. Even someone who does not now nor has ever owned a pet should know 2 people who can vouch for what kind of person they are. Most vets are happy to cooperate. If the answers are positive you can reasonably sure that the same will be done for your pet. If the preliminary screening and reference calls are positive, call the family and make an appointment for them to see your pet.