Got a question about succession

So I started as Whiterun in EK2 and have gotten to the point where I’m High King of Skyrim. Problem is though, the Rift has held out because I married off my current 49yo character to the Queen of Riften a while back. Now here’s the thing: I have a 31yo son of my dynasty who is currently heir to the Kingdom of the Rift, and if he wins, will inherit it from my wife. He’s also in the running for High King of Skyrim but is second to my 22yo brother who is king of Winterhold.

My question is: if I can get my son into 1st place for the elective of High King, will he also inherit the Rift? And bonus question; should I give it to my brother who is younger than my son instead, and then just De Jure conquer it?