I know it's going to be terribly hard to tell your child about this! Pet dogs are part of the family.
That being said, I have to agree with Eggs4Sale. There's a dog 2 houses down the street from me that doesn't like my dog and has come out into the street to start a fight with her even when I'm standing right there. I'm prevented by walking my dog because of their failure to take responsibilty for their dogs.
I'm sorry, but your dogs have obviously been a real, uncontrolled hazard for the mailman and I'm also thinking that he's going to assume that all of your dogs are aggressive as the one that cornered him on the porch. I can't blame him for that. He's taking a chance of a dog attack otherwise.
Many mailmen actually like dogs but are sick of dogs that run out and chase them or attack them. If you'll confine your dogs in the future, talk with the mailman (and maybe apologize for the dogs chasing/attacking him before), let him know that you've got a new invisible fence (or some other means of containing the dogs), you might have him treat your dogs totally differently.
I made a point to introduce my mailman and the dog when I first moved here and had him feed her some treats so that she'd equate him with food and as a friend who was free to come into the yard. I also watched for him and did the same several times that week. As a result, my dog and mailman get along very well. He tosses her treats almost every day, even has her trained to do a trick for him, and he has absolutely no trouble coming in the gate, across the yard, and up on the porch while I'm gone and the dog is out. It's worked for years! I don't ever have to worry about the mailman coming or try to figure out if he's here; my dog lets me know she wants out to great him and get her treat!
Just in case, I also trained my dog to get off the road and lie down in the ditch (no curbs, I live in the country) whether she's off leash or not. I've done the same with the UPS man, who comes here frequently and that's worked well too. If I'm expecting other packages, I leave a small trash bag of treats with a message to the delivery person to feed them to the dog first and if they're still afraid of the dog, to just toss the package over the fence. They've never had a problem with my dog either. My dog still functions as a good watch dog for strangers but neither I or delivery people have to worry about her causing a problem. (Just a note, my dog can clear the front yard fence if she wants to and I let her, but she's never done that to chase cars or attack people. A fence might be good if only to teach your dog where they're allowed to go.)
My point is, there's a number of different things you can do to prevent it happening with a 4th dog, even down to confining the dog when the mailman's expected, most of which will require some time but will definitely be worth it. Hopefully you'll be able to find something(s) that will eliminate the danger for your dog, the mailman, and any visitors to your house and prevent having to tell your child again that someone ran over your dog. That's never easy and it's terrible to lose a dog you love. I hope you never have to go through that sorrow again.
Best wishes,
Ann