Adding to this, it doesn't seem like it was a burning hatred for the sister and I'm on board with that. He himself said it was an "experiment." He wanted to make sure it would work without detection and it did, except the one person who he DIDN'T want to notice, noticed.
He doesn't necessarily need to hate his sister with a burning passion, despite what people might think. Some resentment, mixed with the clinical efficiency of a scientist, is all that's needed to cause tragedy.
I personally love this concept for the uncle. He's been to war, he's a strategist. It makes sense for him to be a bit more detached in his revenge. Having him truly hate those on the throne and simply resent others, with a more clinical approach to trying to destroy them, feels like a subtle twist on a typical cliche.

But i for one am not really
The uncle was shunned by the royal family and was made to renounce his claim to the throne
(which was his birthright + he was a war hero )
All because the former was a r*cist against magic users
I bet if he was still alive when violet awakened her magic she would gotten a similar treatment from the royal family
I also get the uncle killing her mum
Yes she was his sister
But haven't we all read enough stories here where even that is no reason to forgive someone
Especially when that person knew what happened to you, how you were raised and outcast
So yeah i get him hating her
And hating her even more for when her daughter was born with magic she turned around and asked him to be her teacher
As if that wasn't the very thing he was mistreated for
With seemingly no guilt about that
Then there is the current king who only got the throne thx to the former king bullying the uncle into stepping down
Even tho the current king seems to be absolutely mid in comparison to everything the uncle has archived
+ The same thing with violets mum counting for him too
(Its even stated multiple times that the king adores violet)
So some might think
"Yeah but why not kill him then too?"
Because him and his wife being too old to make another heir
+ Him having to watch his son die slowly
Would def be punishment enough
Him having to watch his son the heir of a crown , He only inherit because his older brother was robbed off His birthright,
Be robbed of his crown himself
Is somewhat poetic in a way
So yeah i get the uncle holding grudges for more that half his life ive been mad at other for less lol