I don't know anything about your family's history, but having done a lot of genealogical research, I've found all sorts of name-related oddities like this. Names have a way of getting re-spelled and misspelled by one's descendants over the years. Also, sometimes the person's parents misspelled the name to begin with, wanting to use a name they'd heard but not knowing how to spell it correctly.
(For example, I'm thinking of a great-aunt of mine whose middle name was Suzieann, which likely represented an attempt by her parents to name her Suzanne or Susannah.)
So it is possible that what your great-aunt's children and grandchildren heard as "Rienette" was originally a name such as Renate, Renata or Renita, or that her parents were going for one of those names and did the best they could at spelling it.