"Want to come over to my place for a bit?" "Is that okay?" "Yeah, both my parents work, so they come home late."
Literal
"Little-while home [target-に] drop-by-go-not?" "Good [explanatory-の]?" "Home both-parents-work [copula-で] parents [topic-は] late [explanatory-の]"
Natural three-turn dialogue. 寄っていく ('to drop by on the way') combines 寄る ('stop by') with the ~ていく auxiliary pointing the action away from the speaker. The negative-form invitation ~ない? is a common soft invitation. 共働き ('dual-income household, both parents working') is a common word for the modern two-income family. のの endings sprinkled throughout give it a feminine/conversational feel.