Then how do you usually distinguish between them? I mean in this case how do you tell if this is a new niece or cousin.
Also do you count them all together. If someone asks you "Hoeveel nichten heb je?" would you answer including cousins and nieces or would you ask for clarification or would you generally include one or other category by default?
You just use some more words, saying that you have X neven/nichten and your sibling has X children, or something like that.
Often, people use "nichtje" and "neefje" for niece and nephew, but it depends a bit on how old you are and how old your niece and nephew are.