It just sounds like you need more management with the dog. He had a yard before and space and that helped make up the lack of time spent draining his energy actively on the part of his owners.
Now that he doesn't have that outside space that energy still needs some place to go. Sounds like it has been going into destroying your stuff. If I were you I'd get a crate. Feed him in the crate so that your kids can't screw with him while he is eating or chewing on a chew toy, keep him in the crate unless you are watching him directly. Make sure you are making an effort to supply him with routine and high intensity exercise if you can't invest time in less intensive exercise (and it sounds like you can't your hands are already pretty full.)
I'm glad you didn't over react and put the dog down or something like that.