I observed the following weird behavior of the jarl's housecarl in Dragonsreach with Irileth as the housecarl and Balgruuf as the jarl (but since that behavior comes from HouseCarl alias of DialogueWhiterun quest, this also covers their civil war alternatives):
Between 16:00 and 20:00, Irileth keeps running to Balgruuf until she stands on him, literally. This happens because of WhiterunHousecarlJarlGuardSandbox package in HouseCarl alias which, contrary to the "Sandbox" in its name, is a "follow" package actually. I suggest simply removing WhiterunHousecarlJarlGuardSandbox package from the alias altogether since the Jarl does not leave the throne between 8:00 and 20:00 anyway and the HouseCarl already has a better alternative in the package list right below that "follow" package - WhiterunHousecarlJarlGuardThrone ("stand guard at the throne between 8:00 and 20:00"

.
Between 20:00 and 22:00, when Balgruuf goes to his quarters, Irileth does nothing, standing still at whatever spot she finds herself at 20:00. This happens because there's a gap in the HouseCarl's package list for that period of time. I suggest expanding her WhiterunHousecarlUpAllNight22x8 package ("sandbox at the war table between 22:00 and 8:00"

to 20:00 to cover that gap.