I have the same problem with Kira commanding the Defiant as I do with O'Brien being on the Defiant acting as engineer, yet still clearly assigned as DS9's chief engineer. As well, Cadet/Ensign/Lt. Nog acting as helmsman on the Defiant and showing up as O'Brien's engineering assistant on the station. And really, what is Sisko doing commanding both the station and the ship?
It's all very messy and confusing. In military organizations, a person is stationed to just one place with very specific duties one has been trained to fulfill. When has Kira received training for command of a warp powered ship? Of course, it could be equally asked what training did she receive to be an administrator on a space station?
For me, these sorts of things require the old "suspension of disbelief," but it is quite annoying!