Do nurses have the right to ask family members/relatives to leave if they think are abusive to a patient?

Absolutley! The patient is likely to open up if the abuser is not around. Moreover, the nurse still to maintain his/her safety at the same time.

It depends what you mean by abusive and if it's happening right now. I would talk about the situation with your charge nurse or manager first, and also consider if a social worker or security officer is needed to assist. This is not a solo mission. You have the right to a safe workplace and it's your job to keep your patient safe, and nurses are mandated reporters for suspected child abuse.