Joseph and ZD, I wrote “in uniform”. I did not write “IDF”. During the War of Independence he was a member of the Hagana and also fought alongside the Etzel in Yerushalayim. Actually, while at the start of the war there were three separate underground armies, they very quickly merged and became the IDF (??? ???? ?????? from ????? ???? ?????, ????, ????? ???? ?????). After the war he served for an additional seven years and reached the equivalent rank of Lt. Colonel.
As for how Rav Kook and his son dressed, Rav Tzvi Yehuda said that a rav should dress in a manner that would command respect from his congregants and talmidim. However, he felt that an IDF uniform was really more honorable.