Okay, this dog does not know where he fits in the hierarchy. Start with training, even if it means having a trainer come to the house. And be sure the trainer trains you.
You let him run loose and then you wonder why he's all over the house? He thinks the world is HIS! You need to teach him otherwise.
He needs to be walked on a leash and dried off when he comes in from the mud. He needs to be contained in the house, either through a baby gate or a crate, or both. He needs his own "den" which is his crate. He needs to have toys that occupy him - try a treat ball (he rolls it and little treats drop out), or a chew ball that takes TIME. He needs his toys in a special area. He does not understand that toddlers are wobbly so do not expect him to learn this. He needs to have run-around time outside on a long leash or playing fetch, and then he needs quiet time inside.
Get a spray bottle and put water in it, set on sharp stream rather than light mist. When he runs around or gets on the furniture, goes at the screen, any forbidden activities, squirt him and say NO. Pick 2 or 3 things to work on - don't be squirting him constantly.
He needs to learn that HIS food is in his bowl and your kids need to eat at the table where the dog is not allowed to beg. If the kids walk around with food at the dog's eye level, he thinks it's being offered. When you feed the dog, make him SIT and then STAY (put your flat palm in front of his nose when you say "stay"). Then put his food in his bowl but make him stay until you release him from "stay" - choose a word that you will always use for this. We use "okay" but we don't have little kids who use that word for other meanings. When he sits and stays, say "good dog" and pat his head. He eats when he's told to, not when he feels like it. You can also make him sit/stay for his toys. He needs to learn that you are the boss.
He should sleep in his crate at night, and be there when you are away. When you come home, you have to be thrilled to see him. Do not use the crate for discipline - it's his home, his sanctuary, his bed. Do not let the kids play in it.
You've adopted a dog and then you leave him alone all day - he's stressed and lonely and bored. You chose a large dog (descended from 2 large breeds) who needs a lot of exercise. But you say your children take up your evenings. So what was the plan when you went to get a dog???
If he was in a shelter, he's been abandoned at least once. So he gets adopted, and then you "abandon" him (in his mind) 5 days a week for long hours. He's afraid you aren't coming back and he's acting out. Then when you come home, you are busy with the kids. What's the dog supposed to do? When is his turn? He doesn't know!
He needs training, which comes from love, and discipline, which comes from love. Don't give up on him because you made a poor decision - you are really too busy for this dog, so either commit to training or (with great thought) give him to a family who can spend the time with him.
We rescued a dog who was abandoned at least twice. She took 6 months to really understand expectations but she doesn't deserve to be abandoned again - but we give her the time.
Both shepherds and huskies are working dogs and do well when they understand the expectations. Choose a few behaviors to work on, and be incredibly consistent. If you don't know what you are doing with this type of dog, get a trainer or at least rent a DVD from the library. Our shelter told us not to use "The Dog Whisperer" methods FYI.