@rivetedmood if you want to differentiate the uncle prince from sons of the king, you should use British terminology, which has it covered. The brother of a monarch is called a Royal Prince, and addressed as "His Royal Highness".
They lost a critical point from the LN. She had been sending money home from her salary to help her father keep the family finances afloat, and it had been going instead to try to pay the debts. I don't know why they left that out, here.
there's more emphasis on the romantic parts (although the maid/princess relationship is still quite primary). The uncle is more of a romantic tease for readers though; the more likely ship is between Yulia and the duke's older son.
To add to @Fushiginiku 's points, the novel also mentions
Yulia hasn't seen her family in ages due to strained relations between them (esp. the stepmother) over her job.
Yulia's maid job was originally meant to be a temp position; a badge of honour for an aspiring noblewoman. But Yulia wanted to become a full-time lady's maid because she liked the financial/movement freedoms it gave her, over being a cooped-up, stuffy noblewoman. (Plus caring for Primera.)
An argument broke out between Yulia and the stepmother, which resulted in Yulia leaving the family home.
It's also noted that Yulia's name has not been struck off her family registrar; the final move in cutting off/disinheriting noble children for good.