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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.
Lilibet 'Lili' Diana Mountbatten-Windsor was born on Friday at the Santa Barbara Cottage Hospital in California.
'The whole family is saddened to learn the full extent of how challenging the last few years have been for Harry and Meghan,' Buckingham Palace said in a statement.
Meghan said that her son Archie, now aged one, had been denied the title of prince because there were concerns within the royal family about "about how dark his skin might be when he's born".
The situation is considered similar to the exit of Princess Diana from the palace and the abdication of Edward VIII to marry an American divorcee.
Harry and Meghan's bombshell announcement on January 8 that they wished to step back from their royal duties had rocked the monarchy.
The historic announcement from Buckingham Palace on Saturday follows more than a week of intense private talks aimed at managing the fallout of the globetrotting couple's shock resignation from front-line royal duties.
The 35-year-old Duke of Sussex met with young rugby players in the palace gardens as part of the draw of Rugby League World Cup 2021 while Markle visited a charity in Vancouver.