Middle Grade Siblings Must Survive Alone Base of Mountain

[Therese]

Read as a child in late 70s early 80s. Don't even think it was a chapter book. Purple cover? with very simple illustrations. Siblings (brother/sister) had black hair and were very young. I think the mother was with them in the beginning of the story and then had to go away (perhaps to find help?) and the siblings had to fend for themselves. They kept sweeping the place to keep it clean? When the mother doesn't come back, the brother suggests he go look for her, but then they have decide whether to go together or split up? The illustrations were very simplistic, which makes me think it was for very young readers.