I looked at the site for Medicare. From what I could gather and understand, you have to be licensed at minimum as a CNA (Certified Nursing Assistant). The course is not a long one, but you do get a certificate at the end of the course. And they only pay for 60 days at a stretch. (I think) They do have provisions for long term care. But I really didnt understand what they were saying. And every where I looked they kept refering to an "agency" that provided the personnel. If your parents are covered by Medicaid (the State version of Medicare) the benefits are a bit looser. You would still have to be a CNA, but they usually recognize family members as caregivers and do not require that you be part of an agency. At least that is the way it is here in Massachusetts. You would have to contact Medicaid in MN to get the details. Each State is different.
I feel for you. I am fortunate. My kids are only seconds from me and if I need care, they are right there. My daughter had to take a lot of days off from work to take me to my appointments. That is the main reason I joined my present health plan. They provide all my needs right down to an aspirin at no coast to me or a family member. Good luck. I hope you find a solution.