A source told the newspaper: “Her natural instinct is to try to smooth things over.”
Harry and Meghan are living in California with Archie, who turned two this month, after quitting royal duties in March 2020.
George, seven, Charlotte, six, and three-year-old Louis are not thought to have seen much of their cousin before he moved across the pond.
The Sussexes, who are expecting their second child, made a series of bombshell claims about the royals during their TV interview with Winfrey, which aired in March.
Harry also laid bare his devastating rift with his older brother as he poured his heart out to the US talk show host.
He told Winfrey: “The relationship is space at the moment. And time heals all things, hopefully.”
The row between the once-close siblings is said to date back to the early days of Harry’s romance with Meghan.
Kate then subtly moved away, allowing the brothers to continue on their own.
Ms Tominey said: “Setting aside any personal resentment she may still feel about Harry and Meghan’s televised two-hour tell-all, Kate put her best foot forward in trying to carve a path to reconciliation between the brothers.
“Few would have blamed her for giving Harry the cold shoulder, yet she clearly resolved that the situation needed to be appeased rather than aggravated.”
Harry is due to return to Britain once again in July for the unveiling of a Princess Diana statue.
But tensions are running high with the royals following his fresh outbursts in recent weeks.
The Duke hit out at the Royal Family during an appearance on the Armchair Expert podcast earlier this month.
Harry also lashed out at his family on his new Apple TV documentary series, The Me You Can’t See.