Yuri was born in the slum, daughter to a maid that was actually a honeytrap spy sent by the neighboring country but ends up falling in love with a baron (her dad) and got pregnant.
The mother was chase out of the house after the legal wife found out, and tried to raise Yuri in the slum on her own.
Later on the mother's comrade found the two, and Yuri who wasn't satisfied with her current life and felt she deserved to be somewhere more luxurious than this, studied the art of seduction from said comrade.
After the mom die and the dad came to find her, Yuri use this chance to aim for the queen position + can use her position as the prince's fiancee to weaken the country from inside, making the eventual invasion easier.
Her hatred of Iris is basically jealousy. To Yuri Iris was born with everything. Prestige (duke family), beauty (see: Iris's mom's reputation), wealth (Amelia fief is one of the more prosperous area) and so she wanted to see Iris suffer after losing everything.