I just found this, it’s the older brother.
https://memory-alpha.fandom.com/wiki/George_Samuel_Kirk
I guess so, but it brings up the question in the first ST movie with Chris Pine where the Romulans from the future destroy his father’s starship about where that brother is. The scenes show his pregnant (with James) wife being put in a shuttle to escape from the Romulan ship while the father has to pilot the ship into a ramming course with it, killing him and destroying the ship. There was only the wife and medical attendants on board the shuttle... was the brother off at space camp or something?