“Is my ex-wife required to supply me with items of necessity when my daughter is in my care, such as diapers; since I pay my child support regularly????”
No. Child support generally takes into account the fact that both parents have timeshare with the child. In addition, in order to have timeshare with your daughter, you need to have both the desire and ability to parent. So part of your parenting responsibility is to do and have all the things necessary to have your daughter in your care. This likely includes having all the clothes, food and diapers she needs while she is in your care.
If it was prescription medicine, I would say that should be sent along with the child. Of course medicine would have been a mandatory add-on item that both parents would have paid extra for (over and above base support), anyway.