And Joshua said to all the people, These are the words of the Lord, the God of Israel: In the past your fathers, Terah, the father of Abraham, and the father of Nahor, were living on the other side of the River: and they were worshipping other gods. Jos 24:2
The other Ur, in the south from Joshua's perspective would be on his side of the river, and is not situated between the rivers of Mesopotamia.