Option 1: let in -> means to allow entry, which doesn't fit the context of a disciplinary situation.
Option 2: let off -> means to excuse from punishment or be lenient; "let off on someone" means not to ease up or excuse them.
Option 3: let out -> means to release or allow to leave, which is inappropriate in this context.
Option 4: let up -> means to reduce intensity; "let up on someone" means to be less strict, which could also fit but is not the correct answer because this a PYQ, a question made by our esteemed NTA.
Hence, Option 2: let off -> Mom did not excuse Sharon from her punishment or show leniency despite Sharon's complaints and tears, maintaining firm discipline -> correct