The Duchess of Sussex also claimed Kate Middleton left her in tears during a conversation over flower girl dresses for Charlotte.
Harry also claimed Prince Charles was refusing to take his calls and that their relationship was strained.
"My understanding is that Prince Charles did want to issue a more detailed statement [in response] to the Oprah interview and possibly address some of those issues point by point," Nicholl said, speaking to ET.
"But there was an evening to think about things and in the end, it was decided that a shorter statement would be better, [and] that going at things point by point could be potentially more damaging and give more ammunition for the row to continue.
"I think Prince Charles and Prince William were keen to correct some of the things that the couple had said."
She added that Prince Charles was "particularly frustrated" by the suggestion that he cut the couple off financially.
"If you speak to sources in Charles' camp, that wasn't the case," she explained. "He did continue funding them for quite some time after they moved first to Canada and then to America.
"So yes, I think there was at one point the feeling that they did want to address more than just the issue of race."
It comes after CBS presenter Gayle King said she had spoken to the Sussexes and Harry and William had spoken since the interview.
She told CBS This Morning: "Well I'm not trying to break news, but I did actually call them to see how they were feeling, and it's true, Harry has talked to his brother and he has talked to his father too.
"The word I was given was that those conversations were not productive. But they are glad that they have at least started a conversation.
"And I think what is still upsetting to them is the palace keep saying they want to work it out privately, but yet, they believe these false stories are coming out that are very disparaging against Meghan, still.
"No one in the Royal Family has talked to Meghan yet, at this particular time.
"And I think it's frustrating for them to see that it's a racial conversation about the Royal Family when all they wanted all along was for the royals to intervene and tell the Press to stop with the unfair, inaccurate, false stories that definitely have a racial slant.
"And until you can acknowledge that, I think it's going to be hard to move forward. But they both want to move forward with this and they both want healing in this family. At the end of the day, that is Harry's family."
