This could be the trilogy "L'Autre" by Pierre Bottero, but I don't think that his works have been translated to English (answer per request of @Jenayah).
I read a young adult novel back in high school (so it must have been written before 2009-10)
L'Autre (The Other) is a young adult fantasy trilogy written between 2006 and 2007.
It is about a boy and a girl, who have inherited powers from their family lines, and must defeat a recently freed evil.
about a guy who was a shapeshifter - and I swore he shapeshifted into some type of jaguar. There was a girl involved and while I’m not sure if she could shapeshift as well.
The girl can shapeshift into a panther/jaguar (and other animals, technically, but it comes in the later tomes). The boy can not shapeshift, but he has other powers.
but I do remember the house they stayed at being some type of castle.
Through their bloodline, they inherit a magical mansion/castle, hidden to those not of the bloodline and in a semi parallel universe.
I think there were others in this house/castle thing that could also shapeshift.
They are also other people who have access to the house and can shapeshift, such as Elio, in the last tome. Other shapeshifters in the book include werewolves.
Regarding romance, I think one of the plots (probably tome 2) was partly about a love triangle, but I can't remember it well and haven't read the book in some time. The two main protagonists date throughout the book, and have married before tome 3.