they - Coniah and his mother. He passes from the second person (Jer 22:26) to the third person here, to express alienation. The king is as it were put out of sight, as if unworthy of being spoken with directly.
desire - literally, “lift up their soul” (Jer 44:14; Psa 24:4; Psa 25:1). Judea was the land which they in Babylon should pine after in vain.