This is only my opinion:
She already get over her dad the moment she get kidnapped and almost died but he didn't cared
I don't think the reason why Dorothy is avoiding Ray in this life comes from simple emotions like hate or jealousy. It's a bit more complicated than that..
It was because 'she had killed him'. It would be hard for her to face him again. She has severe insomnia both previous and this life after killing Ray. Imagine murdering someone in their previous life out of hate not to mention that he was her family that genuinely care for her.
She killed countless people but the person that made her regret the most is Ray.
Of course she would feel guilty to receiving that person affectionate in this life so she doesn't want to receive it at all.
To be honest it felt like she's trying to make Ray hate her too. She thinks she doesn't deserve his love. She never received love from her dad or her mom so she doesn't know how to handle one. Unlike Ray who has his dad's affection. Kindness, love something like that is a strange things to her.
She can't live her life lead by feelings. She know it well for herself that good man cannot be good emperor so she always feels uneasy for Ray to be a crown prince. It's not only jealousy but also a concern mixed in. The future of the empire relies on Ray. She weighs the 'duty' as royalty more than the feelings. 'The emperor must bury his heart' that's what she believes
She realized that she suits the position more but couldn't do anything so the frustration would be towards every behavior of Ray that doesn't suitable for a ruler.
The warmth will slowly heal her wounded heart for sure. Like the time she choose to help Ray in the sword contest and ended up hurting herself but still lied to herself that she only did it because it would be better if the useless princess got hurt/ it would be a problem if the crown prince hurt. Even in the time like this she still thinks about her position not her true feelings of worries.
The story was based on the narrator perspective (which is Dorothy) that's why we can't trust everything she thought. Some of them were to justified her actions some to lie to herself.
I understand that bit I still find it annoying when she does it bc she's nice towards the maid,knight and the twins. I get what you are saying but each time when I'm reading this and she rejects his affection I get annoyed
Tbh, I dislike Dorothy. I find it annoying that she's cold to Ray like I would understand it was her first life, but it's her second, and she knows how much he loves her. I get she's jealous, and that's her father's fault, but get over it at this point. You are not a child, plus she killed him already