What rights can the non-custodial parent have to ask the custodial parent while child is with the custodial parent?

If you have joint legal custody, you have the right to be involved in the major decisions involving your child. You should know and be part of decisions for school, medical care, etc. If your co-parent has sole legal custody, you still have the right to be informed of some basic information such as the school you child is attending, the condition of his health and any major medical problems. You may not have the right to have input on these decisions but that does not mean you should be left in the dark.

Read the agreement between you. It may set forth some basic rights.

If there is no court order defining each parent's rights and responsibilities, she can legally do whatever she chooses to do and you have no rights. You need to either get a court order establishing your rights or, if there is an order, you need to get the court to modify or enforce it. You should consult a lawyer for more complete advice about your options.