I believe you are looking for Beware of the Villainess!
It is an isekai where the main character is pulled into an otome world. She is trying to break her engagement with the prince. He invites her over and he is with another lady when the main character is supposed to be there. She yells at him for it which shocks him to the point of tears. This is because each time the prince had done this before the reincarnation event, the woman the main character became, Melissa Podebrat, would blame the women the prince was with instead.
As part of Melissa's scheme to break up with the prince, she takes a blue haired mute beggar to a ball as a pretend boyfriend. A few chapters latter, he is revealed to be a werewolf and a red haired werewolf attacks Melissa's mansion to get at the blue haired werewolf.