Mary

Yes, which is why I believe she faked a pregnancy to get the crown prince to marry her. Without it he would probably have given the throne to Yian and became a carefree playboy (like he was described in his character description)

Yi-an heavily implied someone already had a premarital pregnancy in the royal family (but he would never throw such a tantrum) when he was talking to the Queen Dowager at the beginning of episode 3. Her face suggests he meant her. And it seems the brother would not have gone through with the wedding without a strong incentive...

The drama released a character synopsis for every character.
https://mydramalist.com/781538-wife-of-a-21st-century-prince/discussions/150340-character-descriptions-extra-info

Did you guys see the "white truck of doom" cameo? XD

Also, about the Queen behavior towards Yi-An. You only need to read her character synopsis that rsooinna posted:

"After entering the royal school instead of sungkyunkwan, she actually met her future brother in law grand prince lee ahn before her fiance the crown prince. perhaps because of the thought that they would become family, her eyes often went to him. actually he was the kind of man who would catch your eye even if he just stood still. an indifferent expression, a quiet nature, and the desires hidden underneath it all. somehow it seemed like he was similar to herself too.

Maybe that is why. every now and then she would dare to imagine what it would be like if he was the crown prince. if he was not a grand prince but the crown prince, if he was not her brother in law but her husband, how would it have been.

Whenever her heart grew desperate, yirang reminded herself of a queen's life. her destiny to become the king's woman, become an idol to all women, and become a part of history. "

It's unrequited love/crush on her part.

I think I figured out the reason behing Yian's dig about getting pregnant before marriage.
In episode 4 we find out that his father died 13 years ago, but Yi-An's brother was still the Crown prince when he got married. And the current king is 8 years old. She lied about being pregnant so that he would marry her.

The parents in this drama are horrible. Ugh.

https://www.arakpop.net/

I watched it live.

Yi-an could not wear the baseball shirt at the game but no one is stopping him from wearing it in bed. XD

The post credit scene for episode 4 is cute.

I think he ordered a replacement gift for her at the same shop he bought the first pen.

I fear the sister will reappear and will be instantly forgiven like it is common in kdramas. Ugh.

I hope they reveal the "engagement" next, so that Da Rim can join in the jealousy. :P

Isn't kissing when you switched bodies a bit weird? It is like kissing yourself.

They are half siblings - they have the same biological father. The sister is the ML father's affair child that he just brought home one day.
(Step siblings would mean they only became siblings by their parent marrying, but have no biological relation.)

The sister is so vile. I though that not inviting the FL was bad, but episode 2, just wow.
I really hope they do not try to “redeem” her like a lot of kdrama do. What she did is absolutely unforgivable.

When the "fiancé" was nagging her about not breaking up because she would be divorced before getting married ... I wish she told him she could just become a widow instead. What an asshat.

Half brothers share a parent as in they are biologically related, while stepbrothers are just connected by their parents' marriage - no blood relation.
Kathryn is probably implying that Sunwoo Hae's father was having a second family way before his mother died...

I didn't see her either, but since everything else follows the story, I would bet they will show her setting the fire next episode.