It's a special event related to her loyalty stat. She'll get nabbed no matter what if her loyalty exceeds... uh... 80, I think? I don't remember. The point is, keep her loyalty bellow this value and she'll be fine.
That said, MC's sister doesn't actually have a route with her brother or anything. There's no incest in this game. So her ending up with the king isn't in any way a major problem tbh. I'd say that out of all the girls, she's perhaps one of the most convenient to throw at the king as a permanent part of his harem for extended periods of time.