If the niece is an adult, her aunt can take her anywhere she wants to go.
If the niece is a minor and the aunt has custody, she can take her anywhere she wants, as long as conditions of the award of custody do not limit travel or relocation.
If the aunt is not a custodian of a minor niece, then she can take the niece out of the country only with the permission of the custodian or custodial parent.
Your niece will call you her aunt or uncle.
That's easy cousins.
Your Aunt's niece is you (if you are female), your sister, or your First Cousin.
You are her great-aunt/uncle. She is your great-niece.
You are your niece's aunt, if you are a woman.Any of your sisters who are not your niece's mother are also her aunts.The sisters of your niece's parent who is not your sibling are also her aunts.
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 aunt's brother is either your father or your uncle. If you are a girl, you are always your aunt's niece.
Your aunt's son and her niece are first cousins to each other.
Your niece's son is your great nephew. You are his great aunt or great uncle.
The great aunt is the great niece's baby's great-great aunt.
Your sister's aunt (who is also your aunt) is the baby's great aunt. The baby is a great niece or great nephew of your sister's aunt.
Your sister's daughter is your niece. If you are a woman, you are your niece's aunt; if you are a man, you are your niece's uncle. Your sister's son is your nephew.