As there is no restriction to meet your child on his birthday or any other day, you can very well meet your child as per your desire.
However if the school authorities object to your meeting inside the school complex, then you may have to wait for the child to come out and then take your child to any place of your choice.
Your wife's complaint with the police will not be maintainable because it is a civil matter and also as you are the biological father, you also have equal rights over your child, let she approach court and obtain a custody order.