Hmm, well, if you want to talk real-world history, then it'd be the eldest son.

The other sons would get a 'claim' which means they have some legitimacy to claim the throne as their own.

Meaning that if the current heir (I believe.. Emerin?) were to take the throne, then die, the 2nd son would have a rightful claim to the throne if Emerin did not have a child. If he did have a child but it was a girl, the throne would still pass to the 2nd son of the current lord (so it would pass to King Emerin's brother). If he had a child but it was a boy, it would be possible for Emerin's brother to say 'nah, he's too young, I'm taking the throne' and just never give it back.

So in short there is a bunch of options but only 1 option would be realistic - for Emerin to take the throne if his father dies. 

Lady Julia wouldn't have much of a say in the matter (again, if we're speaking realism. This is an RP so anything can happen) because Emerin is way too old for her to be a regent.