This might help....
I guess what I am saying is that the city of David at the time of David is much smaller than modern day Jerusalem. So the question is - where was the old city actually located on today’s map? then the next question is - when Solomon built the temple was it in the ancient city of David or on the current temple mount? Lots of folks seem to think that the current temple mount is not the original site for the temple at all.
It’s the Temple Mount. The Muslims always try to build a mosque over their enemies Hoky places to signify victory over their enemies.