It is funny how Rosemary is deemed the only problem, even though second prince(I cannot remeber his name even though I’m sure it was stated in the chapter) is a roughly equivalent dumpster fire. Double standards are a bitch I guess?
Kind of yes, though it doesn't really make sense for why they wouldn't. This is an aristocratic society. Marriages/blood ties are what bind the various families together. A guy sleeping around like that, possibly fathering bastard children, especially when he is a royal, is a major issue. Ties to the throne are things that cause problems when they aren't controlled, and even when controlled, it still causes problems. Even without that, that kind of thing still is going to cause problems, because again, blood ties are important and he can ruin some political marriages with his philandering (might be where Rosemary got her groupies from). Which would likely lead to him, and the women he is sleeping with, on the hit list for Serena and her peers.
With the fact that there seems to be a cottage industry of assassins who kill off the corrupt and stupid nobles, you would think that he would be taught to think about what he is doing more. I can understand Rosemary being stupid, even if she comes off as maliciously so at many points, but this guy is being raised by a power hungry woman. Families getting killed off is not something that should fly under the radar for someone like that.