My mother said it looked like rain and brought in the laundry.

Literal

Mother [topic-は] rain [subject-が] come-[appearance-そうだ] [quotative-と] said-[sequential-て] laundry [object-を] took-in

来そうだ = 'looks like it will come' — the appearance そうだ (stem + そう), distinct from the hearsay そうだ. 洗濯物をとりこむ = 'to take in the laundry' — とりこむ = compound: 取る + 込む (take in).