Grandma Has Arrived! Carole Middleton Checks in on Kate and the Royal Baby at the Palace

Grandma Middleton is reporting for royal baby duty!

Carole Middleton arrived at Kensington Palace on Wednesday to meet her newest grandson and to check in on daughter, Kate Middleton.

The famously hands-on grandmother also picked up Prince George from school, while Kate tended to her newest arrival. Dad Prince William took part in Anzac Day memorial service on Wednesday at Westminster Abbey before heading back home to be with his family.

From backup childcare (it was Carole who looked after the kids during Will and Kate’s 2016 tour of India) to setting an example for her three children (Kate, 36, Pippa, 33, and James, 31), the former Carole Goldsmith —who once worked as a flight attendant before founding her wildly successful Party Pieces business with her husband, Michael Middleton — is her family’s rock.

“I don’t think anything fazes [Kate] — she just takes everything in her stride,” a family friend previously told PEOPLE. “A lot of this comes from her mum. Carole’s lovely, and she just doesn’t let anything faze her.”

“She adores being a granny and always tells people, ‘I’m loving it.’ ”

RELATED VIDEO: Prince George and Princess Charlotte Visit Royal Baby in the Hospital

Kate’s dad, Michael, and her younger brother, James Middleton, also paid a visit to the palace, following Pippa Middleton’s lead (the pregnant royal sister was one of the baby’s first visitors on Tuesday).

The royal baby’s great-grandmother, Queen Elizabeth, is currently at Windsor Castle, where Prince Philip is still recovering from hip surgery.

After the baby’s birth, the palace released a statement on behalf of the royal family: “The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news.”

Prince Charles is expected to meet his grandson when he returns from France, where he is marking Anzac Day.

• Watch the full episode of Raising a Royal streaming now on PeopleTV.com, or download the PeopleTV app on your favorite device.

• Watch the full episode of Raising a Royal streaming now on PeopleTV.com, or download the PeopleTV app on your favorite device.

“We are both so pleased at the news,” Charles said in a statement. “It is a great joy to have another grandchild, the only trouble is I don’t know how I am going to keep up with them.”

The new baby, whose name has not yet been announced, also had some visitors before leaving the hospital: Big brother Prince George, 4, who was still donning his school uniform, and big sister Princess Charlotte, who turns 3 in May and adorably showed off her royal wave for the crowd of well-wishers.