The Latin equivalent of the English phrase 'moon's dream' is Somnium lunae. In the word-by-word translation, the noun 'somnium' means 'dream'. The noun 'lunae' means 'of the moon'.
"Malae diem" I belive (Malae = Bad, Diem = Day)
Child Lunae
"The rest of the moon" is reliqua luna.
Luna (-ae, f.)