This question is asked periodically. These answers may help; just tailor them to your specific area and public and private transit service. Google can help locate resources in your area.
So, what kinds of doctors is your mom seeing outside of the NH? In the few instances that my mom has had to got outside for an appointment, we use an ambulette service. But mom's medical care, all of it, is done "in house". There is very little they can't do.
https://www.agingcare.com/search.aspx?searchterm=transportation+to+medical+appointments