No, they do not have any right of the sort. The niece's parents may allow them to visit, but there is no legal obligation to do so at all.
The opposite relationship of uncle would be Niece or Nephew.(The opposite gender is aunt.)
You are a great great aunt or great great uncle to your great great niece (or great grand niece).
Your brother's daughter is your niece, her daughter is your great niece and her granddaughter is your great great niece. It works the same for nephew, aunt, and uncle.
Your sister's daughter is your niece. You are her aunt (if you are a woman) or her uncle ( if you are a man).
Your brother's granddaughter is your great niece and you are her great uncle if you are a man, or her great aunt if you are a woman..
Your niece will call you her aunt or uncle.
You are her great-aunt/uncle. She is your great-niece.
You are an aunt/uncle-in-law! Congratulations!! You really are; because you're an aunt/uncle to your niece you are now an aunt/niece by marriage to her husband.
Your niece's son is your great nephew. You are his great aunt or great uncle.
To your sister's daughter you are an aunt (or uncle) and she is your niece. To your niece's daughter ( your sister's granddaughter) you are a great-aunt (or great-uncle) and she is your grand-niece.
Great great aunt/uncle. To your niece, you are the aunt/uncle, to her child you would be the great aunt/uncle. So you would then be the great great aunt/uncle of her child's child (her grandson)
If you are a woman, you are great great aunt to your niece's granddaughter. If you are a man, you are great great uncle to your niece's granddaughter. In either case, your niece's granddaughter is your great great niece.
A niece or nephew is the child of an aunt's or uncle's brother or sister. So the parents of the aunt/uncle and of the niece's/nephew's parents are the same people - their grandparents. The grandmother of the aunt or uncle is the great grandparent of the niece or nephew.
To your uncle, you are his niece or nephew.
Your aunt's brother is either your father or your uncle. If you are a girl, you are always your aunt's niece.
The opposite relationship of uncle would be Niece or Nephew.(The opposite gender is aunt.)
Your niece in-law, or your niece by marriage.