The mother of my child and I have joint custody. Can she put my daughter in school on my days if I have not agreed to it?

The answer depends on what the court order says. If the court order is silent on school and your child is of an age where she must now attend school, unless the two of you agree, either of you can enroll her in school. Most districts will not permit a child to be enrolled in two schools. It's also generally very hard on a child to have to learn two different curricula from two different schools (and she will presumably miss many tests, field trips, etc. with her classmates when she's basically missing half the school time at EACH school).

If you and the other parent can't decide which school is best for your child's sake, ask a court to make that decision and provide sufficient competent evidence for the court to make the right decision.