Here is a link to the 2006 thread about the evolution of Turnberry that Niall alluded to.
https://www.golfclubatlas.com/forum/index.php/topic,27257.msg516215.html#msg516215It doesn't appear to add anything to the evolution between the WW's.
From other sources I've read, Braid was engaged in 1923 to redo the No. 2 course. The left hand green in the image above is presumably his.
The RR bought out the hotel and golf course in 1926. Some sources say that Hutchison was retained in 1926 to redo the Ailsa course. A new professional, James Macdonald, was also added in 1926 by the new owner. Since it is reported the CKH completed the redesign in 1938, it appears to have taken 12 years to complete the work. However, another aerial from 1930, following, shows that the four CKH holes south of the road, which were new from the Fernie routing, existed in 1930 and appeared to be in fine nick. It would seem that CHK was completed with a lot of his work well prior to 1938.
It is astonishing in these aerial photos to see conditions that appear to be very good even by today's standards. Also the width of the fairways seems quite wide by today's standards.
You can click through the photo to get a larger version.