Can I show the cost of my mother's home care on my tax return?

You would need to contact a CPA or something who does tax returns on a regular basis. Are you declaring Mom as a "dependent" on your return?

My husband is under hospice care in our home, with 3 to 5 visits a week. It's all paid for by Medicare. We never see a bill. I don't know how that was set up and managed, but there's no way we could afford it.

#1 You must file an itemized return.
#2 It must be filed under all of your medical expenses, including dental.
#3 Medical expenses must be over 10% of AGI.

If she is not your dependent and files her own return: NO
If she IS your dependent, see what Llamalover wrote.

#4 She must be claimed as your dependent.

Also, if trying to deduct as medical, then the contract with the agency should be as medical and not as companion/ADL level care. I had Visiting Angels for 9 months, but it was just to be a companion, help with cooking and housekeeping, no medical stuff - she was not allowed to give my mother any medication, or anything like that.