I have a 16 yr old son who's still at school, he's shows no respect to myself or his step mum, or any other kids in the house(4 others) he consistently kicks doors and swears all the time, can I kick him out to go and live with his mum, who would have him, and change his schooling in his last year?

You are the custodial parent and are responsible for him. You just can't kick him out.

However if his mom would like him to come live with her she can apply for modification of the custody agreement and become the custodial parent.