Is there any type of service (free) where people visit people in homes that have no family to visit regularly?

You might try contacting local religious organizations. Would it be feasible to have your Mom moved to a facility closer to one of the kids?

Has she always lived in Tennessee? Perhaps her former neighbors could be prevailed upon to visit occasionally and bring their children/grandchildren or pets. I would also look into the logistics of moving her to a facility nearer to family.

i have a friend that would like to offer her services to stay with an elderly person for several hours a day and be paid for her services. this would be a second job as she has a part time job presently. any suggestions.

if she's in NH there are many other residents she can get to know to fill the void.
Living far away is a great reason not to visit but why not move her to a NH close to one of you ... problem solved!

You say "the cost is killing you" and the home " won't continue to medicate her". Is she on Medicare and/or Medicaid? If Medicare is paying for meds, why won't they give them to her? Can she apply for Medicaid in her state?

Can you provide more information? Why is she medicated? Why can't you and your siblings deal with her? There is far more to this and you need to provide more information. At this point it sounds like you all want rid of her personally, just pay the bills and find someone else to deal with her. Sounds harsh but you gotta come clean here if you want help/advice. It's not a place to look for freebies.