What to do with this psycho cat........?

I adopted a 1.5 year old cat from the shelter about three months ago. He was sooo sweet and gentile at first but he seems to be getting more and more aggressive. I have three young children who are scared of him. He gets in "moods" where he attacks everything that moves. I understand that cats can get very playful but he is scratching and biting. He lunged at my 4 yr old daughter and scratched up her neck. He pounced at my husbands face when he was sleeping. I keep a spray bottle near so I can spray him whenever he does something bad but it does not seem to be helping. I neutered him when I first got him which I thought would calm him down but it seemed to make it worse. Anyway, I'm trying to figure out if this behavior can be turned around or if I need to get rid of him- which I would hate to do. I just can't have him clawing and biting everyone all the time.