Is a child who has mood swings and a bad attitude likely to stay that way grow out of by the end of his teen years?

Hard to say: Maybe, maybe not. See your family doctor or pediatric physician asap. Don't wait until it's too late.

Make it a phase: This could be a passing phase or it could be a more chronic pattern that is forming or has already formed. Make sure they are getting a good amount of attention for the things they are doing right but also make sure the right rules and consequences are in place. Talk with your child's counselor or doctor to make sure you set the right balance.