dog growling at my children when he is laying down

Question
HI! We just rescued a black lab who is a year old and who previously lived with a young child.  We don't know alot of his past, but was told the reason he was given up was because they couldn't afford him any longer.  We have had him a week today and when we first got him, he was very scared, he was transported here in NY from Texas by truck. The first two days he was here, he had growled at my children (5 years and 7 years) when he was laying down and they sat next to him.  Then, he started to calm down and really seem to making himself at home.  Today, my son tried to lay next to him and put his head on his back and the dog growled again.  We immediately told the dog no in a loud voice and made him go sit and ignored him for a few minutes and you could tell he knew he did something wrong.  My question is, do you think this behavior is something fixable or do you think we should surrender him back to the rescue group? I am just nervous and don't want him to bite my children.  Thanks for any help and advice, I appreciate it very much! Jodi.

Answer
You are correct this is fixable. This is a dog that is possessive over his space and may also be that way with food and toys,so for now don't give him any toys,and do not let the children near him when he is eating. now,the best way to fix this is to take the dog obedience school a trainer can work on with the issues you are having,and training is as much about training you as it is about training the dog. Always supervise the dog when around the children at all time,as should be the case with any dog. Dogs are dogs and children are children and you don't know how one will react to the other when you are not around