You have to have patience with a dog when his life gets changed so drastically! You and your kids moving in was a big change for the little dog! You need to try to understand and help the little dog adjust to the changes, in a positive way. I suggest you do some research on training dogs before you go any further! You don't punish a dog for something after the fact because he doesn't realize what he is in trouble for. It absolutely breaks my heart to think of this little guy cowering in a corner, with no clue why this stranger wants to punish him.
I would hate to hear how you "punish" the dog. It sounds like you're simply either not a dog person or just don't like this little dog. The dog was there first and deserves you to be nice to him! He wouldn't be cowering in a corner if he was being treated as he should! If you plan on living with the dog I also suggest you do research on positive training, when "punishing" a dog isn't part of the training!! Maybe try to find out exactly whats causing the problem and go from there. But have a heart and try to have some understanding for the poor little dog and STOP punishing him!! Take up the rug if it that important to you. I'll be praying for the little dog.