There are many children whose mothers go out to work.
Literal
Mother [subject-が] work-[purpose-に] going-out-[ongoing-ている] children [subject-が] many exist-[polite-ます]
母親が働きに出ている is a relative clause modifying 子供達: 'children whose mothers are going out to work.' 働きに出る = verb-stem + に + motion verb (purpose pattern). ~たくさんいます = 'there are many.'