As the surviving spouse of a veteran, your mother may be eligible for a widow's pension. This benefit provides up to $1,094/month to help pay for long term care, including home care. To qualify for the maximum, your mother's home care expenses plus any health insurance premiums, e.g. Medicare supplement policy, need to exceed her income. If she will be spending less than her income, she may qualify for a partial benefit.
Her husband, the veteran, needs to have served at least 90 days on active duty. At least one day must have been during a period of war. He did not have to be overseas or in combat for her to be eligible. He also needs to have received an honorable or general discharge.
Your mother's assets need to be relatively low. A guideline is that her assets should be under $50,000.
You can contact your county veterans service officer or a local veterans service officer at the VFW, American Legion, etc. They can assist you with the application.