Your first cousin's daughter is your first cousin, once removed.
2nd cousin
Second cousins
Your cousin's daughter is your first cousin once removed. Your daughter and your cousin's daughter would be second cousins.
I think the kids would be second cousins
You are one generation out of synch. That would make you first cousins once removed.
I think the kids would be second cousins
They would be cousins.
They would be cousins.
Your relationship would be that of cousins.
Your nephew and your daughter are first cousins to each other. Your nephew's son and your daughter are first cousins, once removed. Your nephew's son and your daughter's child would be second cousins to each other.
You and your mother's brother are first cousins. There is a generation difference between your son and the daughter. That makes them first cousins once removed.
If by cousin you mean first cousin, your daughter and your (first) cousin's son's are second cousins to each other.
Either they are second cousins or technically not related at all. Your cousin's niece would be one of her siblings' children, in which case it would one of your cousin's daughters, or her spouses' niece, in which case there is no blood relationship, but most families would refer to them as a cousin.