This is a personal opinion: I despise people who can't take a hint like how the sister ruined the MC's plans. I'm biased because I hate this in real life and I can't comprehend how someone can be that oblivious since I pick up vibes so easily...
Putting that aside, the sister isn't bad, the same way the prince isn't necessarily bad...he is a fucking prejudiced holier than thou imbecile (I can't get over the time he accused her during that tea party without listening to anything that is going on around him) but he isn't like the usual mean princes who want to dump their fiancés and are purposefully being malicious....I think both him and the sister suit each other in their stupity but the country is doomed is they're future king and queen. The sister reminds me of the blond bitch from "The Evil Lady Will Change" but the sister from that one is much much worse and if the sister in this one is a 6/10 on the annoyance/pedastal scale, that one breaks the fucking scale.
Anyway, I think these characters serve their purpose as they are made to show how reasonable the MC is and that being naive doesn't equal being good. Also, they are made to put off the happing ending because I'm sure the MC and Yulan would've made more progress romantically, and the MC would've had a better family if they didn't exist ( Same applies to Yulan, concubine son or not, if the prince didn't exist Yulan would'nt have been bullied for being second in the hierarchy or princes)