Dorico copies music “instrument by instrument” not “staff by staff”.
If your imported file has two single-staff instruments, it will try to copy it to two instruments, and since the “correct” piano part only has one instrument, so the music for the second instrument is not copied.
Select the music on one staff at a time, and copy it to the correct staff on the new piano part.
If the music on one staff is being split between the staves, do you have a “split point” set for the second piano?
(Sorry, but I never use split points because I don’t write the sort of notation where they are useful, so I don’t know exactly how they work).