I am trying to find out information of who took personal care of Sir George Rooke's son - George?
George was born July 1702, and passed away Nov. 1739, and was only 6 1/2 when his father died.
Beyond finding the identity of his legal guardians, whose names you've now been given on another thread, I suspect you're unlikely to find more details about this in his father's will.
You may already know that young George was admitted a fellow-commoner* of Pembroke College, Cambridge, on 21 March 1717/18, at the age of 16; Bachelor of Arts, 1719/20 (Venn,
Alumni Cantabrigienses) ...
https://venn.lib.cam.ac.uk/Documents/acad/2018/search-2018.htmlSo, if you contact the archivist at Pembroke College, they will probably be able to tell you whether he previously attended a public school (and, if so, which one), or if he had a private tutor.
Contact details for Pembroke are on this page ...
https://www.pem.cam.ac.uk/college/library/archives-special-collectionsADDED
Venn also says he married
Frances Ward (daughter of John, Viscount Dudley), died without issue 24 Nov 1739, and was buried St Paul’s, Canterbury (from a published notice in
The Genealogist, iv, 198, which I daresay might be found online somewhere).
ADDED
*
Fellow Commoner - originally an affluent, usually aristocratic, student granted among other privileges that of sharing with the Fellows of a College the amenities of the high table
(
https://www.lib.cam.ac.uk/university-archives/glossary)