Kim Kardashian Is 'Attempting to Be Respectful' of Kanye West But Has 'Moved On,' Says Source

Kim Kardashian Is 'Attempting to Be Respectful' of Kanye West But Has 'Moved On,' Says Source
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Kim Kardashian West is proceeding to focus on her co-parenting relationship with ex-Kanye West in the midst of the rapper's public requests for her to reunite with him.

While performing at the Free Larry Hoover show Thursday at the Los Angeles Coliseum, West, 44, committed his tune "Runaway" to Kardashian West, 41. In the wake of singing the verses, "I want you to run right back to me, child," he added, "all the more explicitly, Kimberly." The move was the most recent in a progression of articulations he has made about needing to rejoin his family.

A source tells PEOPLE that Kardashian West "realizes where Kanye's head is" yet "disregards it." The source says Kardashian West "has moved on" yet "she knows it's hard for Kanye to manage." Says the insider: "She isn't amazed that he argues in broad daylight for her to run back to him. She is simply attempting to be deferential with regards to it."

Related: Kim Kardashian files to be Legally Single despite Kanye's several Public Pleas

Kardashian West went to the Thursday show with her sister, Kendall Jenner, and her mother, Kris Jenner. She additionally carried along with two of her youngsters with West: North, 8, and Saint, 6. The previous couple is additionally guardians to girl Chicago, 3½, and child Psalm, 2½.

The source says that oldest youngster North "is particularly an enthusiast of her father's music" and Kardashian West needs to ensure her children approach their father and his occasions. "Kim will continually carry the children to occasions that are vital to Kanye," the source adds. "Co-nurturing and ensuring her children are glad will consistently be her need."

RELATED: Kanye West pleas ex Kim Kardashian singing 'Run Right Back to Me' at Concert

Kardashian West sought legal separation from West in February after almost seven years of marriage. The team started dating in 2012 and later married in 2014.

The SKIMS organizer has as of late been dating Saturday Night Live joke artist Pete Davidson, whom she's been connected to since they were captured clasping hands at Knott's Scary Farm in Buena Park, California in October.

A source told PEOPLE last month that Davidson is "precisely" what Kardashian West required in the midst of her separation from West.

"He's by and large what Kim required after her separation — somebody to make her snicker and simply have a good time with," the insider said. "The finish of her marriage was an extremely dim time for herself and Pete has been the best antitoxin. They have been getting to know one another rapidly," the source added. "Kim likes him to an ever-increasing extent."