My niece is going to have a baby. what will the babys relationship be to me/ what is the difference betwee, say a nephew once removed and a 2nd nephew?
The baby will be your great-nephew or great-niece. There is no such thing as a nephew-once-removed, nor is there such a thing as a 2nd-nephew. You are probably thinking of a cousin once-removed, who is the child of your cousin.
How lovely! You must really be looking forward to this new little relative. Do let us know what it is when it arrives. You could put it like a question..eg "Who thinks it's wonderful that my neice has had a little boy/girl?"
Good luck!