Prince William and Duchess Kate Celebrate 4th Wedding Anniversary as World Awaits Second Royal Baby

— -- How do you spend your fourth wedding anniversary if you're the most famous couple in the world, waiting for your second child to be born? Some newlyweds celebrate the traditional way with fruit and flowers. Britain's Prince William and Duchess Kate went back to where it all began today.

Four years ago the Duke and Duchess of Cambridge said "I do" in a lavish, royal wedding watched by millions around the world. They kissed not once but twice to the cheering crowds with 2 billion well-wishers around the world watching.

Today, it was a decidedly simpler affair. Kate and William slipped into Buckingham Palace with their nearly 2-year-old son, Prince George, to spend some private time as a family before the new baby arrives and makes four.

Kate, 33, has said that she is due to give birth to the couple’s second child anytime between mid-April and the end of the month. Despite being past her due date, Kate was spotted going about business as usual.

Photographers caught a rare glimpse of Kate Tuesday behind the wheel of a Range Rover driving George to the swimming pool at Buckingham Palace. A security officer was spotted in the passenger seat while George and his nanny were presumed to be in the backseat.

Kate and William have been teaching George to swim inside the Queen's home. With Her Majesty The Queen away in Windsor today, the family had the place to celebrate and for a second day in a row entertained George by the pool. And perhaps, as some medical experts have suggested, swimming could help Kate's labor come sooner.

Buckingham Palace is just a short drive from Kensington Palace, where the family has been stationed as they await their new addition. Kensington Palace is located near St. Mary’s Hospital, where Kate is expected to deliver in the hospital’s private Lindo Wing.

After the birth, the family is expected to spend some time at Kensington Palace before moving on to their 10-bedroom country estate at Anmer Hall in Norfolk.

Royal sources say the couple does not know whether they are having a boy or a girl. Speculation peaked that a princess could be on the way Tuesday morning when fans camped outside St. Mary’s Hospital received boxes of pastries and croissants from the royal couple, tied up with a pink ribbon.

“The Duke and Duchess wanted them to know they were thinking of them,” a Palace official told ABC News of the generous gesture. "They saw they had been camped out and wanted to send over some breakfast."