She spoke with her mum Marian and brother Craig Robinson during the podcast episode.
Ms Obama explained that her husband would shuffle his presidential schedule in order to create some normality in his daughters’ lives.
She said: “Even as Barack being the President of the United States, he worked his schedule around their schedule.
“They weren’t waiting until 9pm to eat because dad was running late.
“They never couldn’t not go somewhere or do something because of dad.
“I never wanted them to resent the presidency, or resent what their dad did.”
During their eight years at the White House, Ms Obama’s mum moved in to help look after the two daughters.
Her mum told the podcast: “I think the girls did really well with what they had to deal with.
Before moving into the White House, the Obamas lived in Chicago.
During an interview on the Today show in the US, Ms Obama explained why it was vital that her daughters were protected.
She said: “I tried to make sure that they weren’t out there to be crushed.
“But oh gosh, it’s the mamma bear within us.
“We tried to set up boundaries within their exposure which is why you would rarely see the girls outside public events.
“There were a set of things where we told the press the girls are going to be here, this is the time. But don’t go to their school.”
Ms Obama confessed that she felt guilty when her children were exposed to challenges from having a father who was the president.
She said: “But you want your kids to grow up normal and you want them to have these wonderful experiences privately, and you want them to be able to fail and stumble privately, like any other kids.
“And when they aren’t allowed to do that it’s unfair and you feel guilty as they didn’t choose this life. You go through all kinds of emotions.”