The long-lost cousin's daughter would be a first cousin once removed and her kids would be a first cousin twice removed.
This is actually pretty timely as I've been looking up some long-not-seen cousin and have been contemplating the same question. Without the simple grandparent rule, I had to wonder what the order of operations would be.
Since my kids are first cousins once removed from my first cousin, whose kids are my first cousin's cousins once removed, are they first cousins twice removed [cousin(removed + removed)] or second cousins once removed [(cousin + cousin)removed] or second cousins twice removed (cousin + cousin)(removed + removed)
The grandparent rule makes it all a lot easier.