Daughter was injured first day at new school by a teacher - Any legal recourse?

The first question is the severity of your daughter's injury.  If the injury is relatively minor, then the cost to pursue a claim might well exceed your recovery.  You also need to factor in the cost of quitting your job to home school your daughter.  The cost would also include the effect of isolation from other children on your daughter. Unless the injury is severe, you may end up losing more than you would gain. While others may disagree with me, IMO by sending your daughter to the school, you may have implicitly agreed to the terms even though you did not sign the forms.  In any event, the issue is not whether the teacher applied physical restraint, but whether the teacher negligently applied physical restraint.  Teachers have an inherent duty to protect students from harm. So, yes, you do have recourse.  You can engage an expert to evaluate the teacher's conduct.  You can submit a claim for the injury.  Whether you elect to proceed is really a question of what can be gained set off against the cost and potential other consequences.