In fact the books say that it's often the owners who create separation anxiety problems by making a huge fuss over their dogs when they leave or return. So your dogs pick up on your anxiety.
Before I leave, I safety proof the area my dogs are going to be left in just in case they do something stupid and end up injuring themselves. I leave the radio on playing calming music, plenty of water and their box of toys. Then I slip out quietly without a fuss. But it is always a relief to return to find my dogs and my house all in one piece. But of course don't make a big deal about the fact you're back.
My dogs need to learn to cope with spending time alone because I can't always be there for them. So I was advised to start off with short periods of time alone eventually building up to longer periods. I recently asked my neighbour how my dogs reacted when I left. She said there was a bit of whining but they soon settled down. One way to check up on how they are behaving!
Another tip is never leave their collars on while you're away if they still rumble in the jungle with each other. Apparently some nasty accidents have happened with dogs been strangled by collars that have hooked onto something. It is also important that your dogs have time away from each other because you never know when you might have to leave one behind. I learnt the value of this when I had to rush to the vet and leave one of my pups at home. Both survived unscathed.
So don't stress when you leave the kids home alone. If you have taught them to cope from an early age, they will be OK.