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The first show will focus on cooking, gardening, while the other will follow the U.S. Open Polo Championship.
Meghan describes how hard it was for her to land a steady job.
The animated series tells the story of a 12-year-old girl inspired by influential women in history.
The couple had visited the Duke and Duchess of Sussex at their house last week, where Priyanka Chopra introduced her boyfriend to her friend Meghan Markle and Prince Harry.
The couple decided to buck the royal tradition for fruitcake and instead opted for a lemon and elderflower creation with buttercream icing, topped with fresh flowers.
The abuse is often made against one Duchess by supporters of the other.
The image posted Sunday on Instagram showed Meghan's hand cradling the feet of her son, Archie Harrison Mountbatten-Windsor, with a bed of spring flowers below serving as the background.
Britain's aggressive press at first welcomed Markle, 38, into the royal fold but coverage has become increasingly hostile, with the tabloids luxuriating in stories about Markle's fractured American family and rumours of palace rifts.
She wore a sari with shades of blue and green and also sported a traditional tilak on her forehead.
Unlike her sister-in-law, Kate Middleton, Meghan Markle clearly shows the world that she would not completely follow the royal traditions.
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