Caitlyn Jenner has received wide-ranging support from many since she made her debut on the cover of Vanity Fair on Monday, and she can count her four older children among her supporters despite their past relationships.

Jenner acknowledges in the cover story for the July issue that he and his older children - Burt, Cassandra, Brandon and Brody Jenner - have shared a tenuous relationship with her over the last 30 years.

"I have made a lot of mistakes raising the four Jenner kids," Caitlyn told Vanity Fair (via E! News). "I had times not only dealing with my own issues but exes. [It was] very traumatic and there was a lot of turmoil in my life, and I wasn't as close to my kids as I should have been."

She has two other biological daughters, Kendall and Kylie, with his third ex-wife, Kris Jenner. Her four stepchildren include Kourtney, Kim, Khloe and Rob Kardashian.

Caitlyn first tried to transition in the late 1980s. During that time, Cassandra found a parent that was more caring and loving, and "was moving towards his authentic self."

The eldest Jenner sister said she "would have happily traded a distant father for a loving, involved mom." Her older brother Burt added, "I have high hopes that Caitlyn is a better person than Bruce. I'm very much looking forward to that."

Despite the children's support for Caitlyn, they are refusing to take part in her E! docu-series that will premiere on Sunday, July 26. They disagree with her using the same production company as "Keeping Up with the Kardashians" as well as a few of the same producers for fear that Caitlyn's story will be exploited, according to Vanity Fair (via Business Insider).

"You go on E!'s website, the Bunim/Murray website, and you look at all the shows, every one of them is a circus," Brandon said. "With Bunim/Murray and E!, it's been the opposite of inspiration. Oh my God, we're diving into the lion's den - they're gonna make a show about the Jenners versus the Kardashians."

Caitlyn has a more optimistic outlook as she will also serve as an executive producer. She believes she can keep the show from straying toward that "circus" and tell her inspiring and informative story the way she wants.

E! Programming Chief Jeff Olde also wants to put on that type of show and describes the new series as "so far beyond television, on a personal level," especially for him as a gay man and gay-rights activist.

"If I get one thing right in my professional career, it will be this," Olde said. He also reiterated that the goal for the show is not ratings, but "to tell Bruce's story the way he wants [it] to be told."