If your pet is good with kids, and you decide to move forward with an in-person meeting, ask the adopters to bring their kids with them. Observe the way the kids interact with your pet, and the way the parents guide them. Do they let their kids mistreat your pet? If they intervene, are they kind to their children, or do they yell at them? You can tell a lot about how someone will treat a pet by the way they treat their children.
Also, watch how your pet reacts to the children. Pets often give off subtle signs of nervousness or discomfort, such as lip licking or yawning, or not-so-subtle signs, like actually trying to avoid the children.
If your pet isn’t good with kids, and the adopter has them, go no further and politely decline their application.