It absolutely is your right. Keep in mind these people love to lord their authority over anyone they think they can. If I were you my first step would be filling a formal complaint against the hospital. The administration may fire them. If that doesn't work complain to the state nursing board and they will likely investigate.
Whatever you choose to do it sounds like you were in the right here. Don't let them get away without answering for this.
When my youngest was about a year old he was very sick and had a seizure. The ambulance took him to a hospital that was further away because the er doctor at the closer facility recommended they not come there. This was an emtala violation. That doctor was suspended and the hospital paid for the ambulance bill.