Good advice above. I would systematically count the diapers used and see how many she uses during her shift. Also, keep some baby rash cream on the changing table and ask the nanny to apply some with each diaper change. That is what my employers ask me to do and I do it faithfully.
The fact that your baby's diaper rash only comes when in the care of your nanny is disheartening to me.
If in fact your nanny is lying to you and/or making up excuses, then imagine what else she is lying to you about OP. Not to be extreme, but this is your baby she is caring for. She should be 100% honest and upfront about EVERYTHING related to your child. I know I always am to my employers.
When caring for infants, I always check their diapers at least every two hrs. Even more so in cloth diapers since they do not absorb.