The son of Sir George Rooke - George Rooke (1702-1739)

[Maiden Stone]

Above 'horselydown86' explains that: - 'he gives to his then wife Power (3rd wife Catherine) to dwell in my Mansion House of Saint Lawrence, till my Sonn attaine the age of one and Twenty years if she shall be unmarried'.

I'm unaware if she remarried.

Information about Catherine's next marriage was posted by djm297 reply #51 and Top-of-the-hill reply #59 and possibly by others.

Many members of the Rooke family are on a website about genealogical links of a family called Ashe. There are errors with some dates e.g. a Rooke who was M.P. for a century and after he died!
https://www.ashefamily.info/ashefamily/surnames.htm
I was impressed by baby George's godparents, Queen Anne and Prince George! I assume Prince George was the the queen's husband, Prince George of Denmark.

[Calpe 1704]

Above 'horselydown86' explains that: - 'he gives to his then wife Power (3rd wife Catherine) to dwell in my Mansion House of Saint Lawrence, till my Sonn attaine the age of one and Twenty years if she shall be unmarried'.

I'm unaware if she remarried.

Information about Catherine's next marriage was posted by djm297 reply #51 and Top-of-the-hill reply #59 and possibly by others.

Many members of the Rooke family are on a website about genealogical links of a family called Ashe. There are errors with some dates e.g. a Rooke who was M.P. for a century and after he died!
https://www.ashefamily.info/ashefamily/surnames.htm
I was impressed by baby George's godparents, Queen Anne and Prince George! I assume Prince George was the the queen's husband, Prince George of Denmark.

No discredit meant to djm297 nor to Top-of-the-hill.
Marriage proved with thanks. So we can see that Admiral George's 3rd wife remarried just under 2 years after his death, on the 26th Dec. 1710. This being the case she would have needed to leave the Rooke home, as per the Will?

Back to George and his life..

[Top-of-the-hill]

  Lady Catherine may have already left St Lawrence House, as her marriage shows her of St Stephens parish on the opposite side of Canterbury and she married there.
   

[Maiden Stone]

Ursula, Mary, Ann & Jane were aunts. Thomas & Finch were uncles.

For interest, and to rule out young George living with Uncle Finch:

"1696. An inquisition is taken before the Coroner of Can-
terbury on view of the bodies of Anth. Buckeredge and
Finch Rooke, gents, who were both killed in a duel fought
by them with swords, in the North-Holmes, in Northgate,
Canterbury."

Finch Rooke and Anthony Buckeridge were both garrison officers. Information about Finch's death + other Rooke family members in St. Paul's church section of "Historic Canterbury" website. Scroll further down page for extra detail about Finch's duel and death.
Uncle Thomas was also dead. Captain Thomas Rooke died 1701.
Dame Jane Rooke, widow of Sir William (young George's grandmother?) died 1711.
 machadoink.com/st%20Pauls%20Church.htm

An executor of Captain Thomas Rooke's will was sister Mary Blashford.
https://www.ashefamily.info/ashefamily/surnames.htm

[Calpe 1704]

Ursula, Mary, Ann & Jane were aunts. Thomas & Finch were uncles.

For interest, and to rule out young George living with Uncle Finch:
"1696. An inquisition is taken before the Coroner of Canterbury on view of the bodies of Anth. Buckeredge and Finch Rooke, gents, who were both killed in a duel fought by them with swords, in the North-Holmes, in Northgate, Canterbury."

Finch Rooke and Anthony Buckeridge were both garrison officers. Information about Finch's death + other Rooke family members in St. Paul's church section of "Historic Canterbury" website. Scroll further down page for extra detail about Finch's duel and death.
Uncle Thomas was also dead. Captain Thomas Rooke died 1701.
Dame Jane Rooke, widow of Sir William (young George's grandmother?) died 1711.
 machadoink.com/st%20Pauls%20Church.htm

An executor of Captain Thomas Rooke's will was sister Mary Blashford.
https://www.ashefamily.info/ashefamily/surnames.htm

Fascinating information of the two uncles and one aunt.
This link doesn't work - machadoink.com/st%20Pauls%20Church.htm

Back to young George and his life....

[Top-of-the-hill]

  Just google machadoink - I often find myself on that website, it is a mine of information.
 Does the Ashe family site have Mary Rooke's marriage to Mr Blashford? I can't find it. Wondered if she was widowed.

[Maiden Stone]

  Just google machadoink - I often find myself on that website, it is a mine of information.
 

I first found it by searching for Finch Rooke, then by googling Historic Canterbury.
I can't help thinking that Finch Rooke is a hybrid bird.  I know Finch was a maiden surname but did his parents not consider the teasing their son would have to put up with?

[Calpe 1704]

  Just google machadoink - I often find myself on that website, it is a mine of information.
 

I first found it by searching for Finch Rooke, then by googling Historic Canterbury.
I can't help thinking that Finch Rooke is a hybrid bird.  I know Finch was a maiden surname but did his parents not consider the teasing their son would have to put up with?

George Rooke's uncle, named Finch. Finch is actually quite a common Boys first name.

Back to young George Rooke and his short life of 37 years, passing away in Nov. 1739

[Maiden Stone]

There is just no written text about the son George Rooke (1702-1739, that i can find.
His mother died at birth in 1702 and his father, Admiral George Rooke was away often.

However, the father remarried again to a Catherine Knatchbull in 1706, so i suppose that the young George lived with her, he then being only 4 years old, but there is nothing to confirm this.

Upper-class people tended to have more than 1 residence at a time. There might have been a house in "Town" and a house in the "Country". Depending on the man's position in society, his wife may have spent long periods in "Town", running the town-house, entertaining her husband's guests and socialising. Children may have spent the greater part (or all) of their time at the country home, which was generally a healthier place for children, perhaps looked after by staff (nursemaid, governess, tutor).*
It's possible that Catherine didn't have much to do with her stepson. It may have depended on the admiral's purpose for marrying Catherine -  was it for money or social or political connections, or to breed more children or to act as a social hostess or to be a stepmother, or even for love.
Jane, the admiral's mother, was alive until 1711. She may have been overseeing her grandson's care while his father was away.

Added. *As suggested by Top-of-the-hill reply 59.