Tristan Thompson Isn't Living in His Cleveland Home with Khloé Kardashian and Baby True: Source

Insiders have told PEOPLE that Khloé wants desperately to return Los Angeles to be with her family

Just because Khloé Kardashian is remaining in boyfriend Tristan Thompson‘s home in Cleveland for the time being doesn’t mean that they’ve fully reconciled after his cheating scandal.

A source tells PEOPLE that Thompson, 27, is not living in his house with Khloé, 33, and their newborn daughter True, though he comes and goes to spend time with his daughter. In fact the source says that the Good American designer has very little to do with the basketball player.

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Khloe Kardashian/Instagram

Other insiders have told PEOPLE that Khloé wants desperately to return Los Angeles to be with her family but must wait due to her doctor’s orders. Sisters Kourtney Kardashian, Kim Kardashian West and Kendall Jenner flew to Cleveland for a quick trip Tuesday to celebrate Kourtney’s birthday early, but they’re now back in L.A.

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Khloé welcomed her first child, a baby girl, with Thompson on Thursday — just days after allegations surfaced that the Cleveland Cavaliers power forward was unfaithful to the reality star throughout her pregnancy.

RELATED VIDEO: Khloé Kardashian Shares Daughter’s Name Days After Giving Birth Amid Cheating Scandal

Still, the couple put on a united front in her Instagram post confirming True’s arrival.

“Our little girl, True Thompson, has completely stolen our hearts and we are overwhelmed with LOVE,” Kardashian wrote. “Such a blessing to welcome this angel into the family! Mommy and Daddy loooooove you True!”

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