Kate Middleton’s late April due date is fast approaching, but before she gets there, the Duchess of Cambridge, 36, has a surprise waiting for her. “Meghan Markle is throwing Kate a no-expense-spared surprise baby shower with the help of [Kate’s sister] Pippa,” a royal insider exclusively tells Life & Style. The shower will take place at Kensington Palace in London, where Kate, Prince William and their kids George, 4, and Charlotte, 2, live — and where Meghan resides with Prince Harry — and it will be a small affair, with just 10 of Kate’s closest friends and mom Carole in attendance. Kate’s soon-to-be sister-in-law, Meghan, 36, “is spending a fortune on gifts,” the insider adds. “She’s getting everything from Tiffany jewelry to Dior baby clothes.” Meghan has other events on…