I am a member of a beagle rescue out of Newfoundland and we don't have any problems giving dogs that are great with children to families with kids. Especially ones that have such a special way with animals as you describe. We have also in recent memory adopted a beagle to a police officer (we see them as fairly responsible). Is there nothing else you can think of that would set off a rescue. Did they do an interview with you on the phone or at your house. I hope they at least called you. If they didn't maybe your job is setting off alarms in one of those disreputable agencies.
I kind of take issue with the article on petfinder at the top of this post. We would never give out the home address of our foster homes to anyone giving up their dog. What if they changed their mind and came over demanding their dog back. That would put our foster homes in a very uncomfortable position. We also have found it is much better for the dog to be picked up from its home as opposed to being dumped at someone else's house and abandoned. There seems to be less stress on the dogs that way and they settle in better.