In most leases there is an implied warranty of habitability. This warranty imposes an obligation upon a landlord to maintain the premises in such as manner as not to affect the health and safety of its occupants. Things subject to this warranty would be rodent infestation and mold. Regardless of whether the owner wants to fix the property, he most likely has an obligation to do so.
You need to provide your property management company and the landlord with a written request to fix the problem. Send it by first class and certified mail so that you have proof you mailed it. In some states, such as Maryland, if the landlord does not act within a reasonable time to correct the problem, you can pay your rent into a court escrow account.
Moreover, you may have other causes of action against your landlord if you can show that your daughter's sickness is directly related to the mold in the apartment and the landlord knew or should've known about the mold.
Please do yourself a favor and consult with an attorney in your area.
DISCLAIMER: Brandy A. Peeples is licensed to practice law in the State of Maryland. This answer is being provided for informational purposes only and the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, I strongly urge you to consult with an attorney in your area.
See an AZ landlord tenant attorney immediately. You have several issues and there are a number of questions that need to be asked and answered before one could give you your best way-ahead.
READ THIS BEFORE CALLING OR EMAILING ME: I am licensed to practice before the state and federal courts in Virginia. Addressing your issue does not create an attorney-client relationship and I AM providing you educational information NOT legal advice. You should speak with an attorney to whom you have provided all the facts, before you take steps that may impact your legal rights. I am not obligated to answer subsequent emails or phone calls unless you have hired me. I wish you the best of luck with your situation.