Children on flights- can I be kicked off for bad behavior?

Absolutely. They have not only the right but a responsibility to control behavior on the plane and to make it a safe place. As the child's parent if they take the child off, you go too.

The child you describe is not mature enough to handle plane travel. Either make other arraignments or see a doctor for information as to why this child has so out of control and how you can get control back. Either way, the child you described would have made everyone else on that plane not only uncomfortable but angry... Airplane travel is not a right. It is a Privilege, one you and your child will need to earn.

Good luck.

Aside from the obvious disrespect to fellow passengers and the crew created by such a situation, the federal aviation regulations provide that the pilot in command of any flight (including commercial) has the authority to do whatever is necessary to ensure the safety of the flight. If your child is unwilling and you are unable to make the child comply with basic safety regulations (stay in your seat when seat belt sign is on, etc.) the PIC not only has the authority but I would suggest he/she has the obligation to remove you and your child from the flight because of the potential danger to the child, you and other passengers during an emergency situation.
Before practicing law, I was a pilot for a major airline and we would not hesitate to remove passengers for their inability or unwillingness to follow safety regulations.