In joint custody, both parents have legal custody with one parent designated as the primary residential parent. Joint legal custody means that both parents have the right to make major decisions for their children. These decisions can include residence of the child, medical and dental treatment, education, child care, religious education, extra-curricular activities, summer camp and recreation.
Does your agreement speak to the issue? It may. Read it. Generally, though, unless you are being unreasonable, you can have a say in choosing the daycare provider. Your wife can also choose to fight you on it in court.