'sleep in' means to sleep later than usual in the morning. It also implies that 'you' will do some of the mother's early morning jobs.
Sleep in meas to Sleep later than you nowmally would on a specific day or time.
The phrase "sleep in" often refers to the act of staying in bed and sleeping later than usual, typically when one has the opportunity to relax and not wake up at their regular waking time. In this context, "let your mother sleep in" means allowing your mother to have a longer and undisturbed sleep in the morning, ensuring she gets a well-deserved rest and a break from her usual responsibilities.