Khloé Kardashian is "very happy to be with her family": source

Khloe Kardashian stays in Los Angeles – for now.

A source close to The amazing Kardashian family The star tells PEOPLE that she is "very happy to be with her family in Los Angeles" and that she has not considered moving to Ohio with her daughter, True Thompson, aged 6 months, while she was planning to join her boyfriend Tristan Thompson in Cleveland, where he plays for the riders.

"Khloé looks great," says the insider. "She is still in L.A. with True. There have been no further discussions about moving to Cleveland. It seems she is not coming back for the moment.

On Friday, the Corps of revenge host, 34, is joined to his famous family to love his granddaughter. "True had the most beautiful six-month party with its youngest cousins," said the source.

Kylie Jenner's daughter, Stormi, 8 months old, Kim Kardashian West's children in Chicago, 8 months, and Saint, 2, and Rob Kardashian's daughter, Dream, 1, were hung together on a blanket picnic. a variety of sprinkled desserts.

RELATED: Khloé Kardashian organizes the cutest celebration of the "Cousin Cake" on the occasion of the half-birthday of Baby True

As for Thompson, 27 – who seemed to have missed the festivities – the future of their relationship remains unknown six months after his fraud scandal.

"She did not really talk about Tristan," the source said. "She is gushing about True and is happy to work, but that's all."

A few days before True's birth on April 12, Thompson's alleged infidelities made headlines. Since then, Kardashian has been committed to raising her daughter and restoring her relationship with the Cavaliers player. Earlier this week, she traveled to Cleveland for two days without True, and then returned to Los Angeles Thursday morning, a second Kardashian source told PEOPLE.

"Khloe is stable, happy and very happy to be a mother and see how things are going with True," said the source. "As for Tristan, there is still a lot going on between them. Things seem more unstable in the relationship right now, but she has understood everything. "

Tristan Thompson and Khloé Kardashian

Jerritt Clark / Getty Images

RELATED: Khloe Kardashian's relationship with Tristan Thompson is "in the air," says source

Nevertheless, October 12 is certainly a bittersweet day for Khloe. She has told her life since the scandal on Instagram Stories by sharing two enigmatic messages.

"In 6 months, you can be in the same place or in a better place," reads the first message. "Concentrate each day on improving your health, your wealth and your happiness. It will take time, but you can do it.

In the second article, Khloe shared: "You become a master of your life when you learn to control where your attention is going. Value what you give to your energy and time. "

Khloe spent the summer with Thompson and True in Los Angeles, alongside his famous family.

"She is still struggling with Tristan's cheating," the source added.

"She has good weeks when she's fine and weeks when she's upset," a source told PEOPLE.

"It's hard to trust 100% of people who cheated a few days before becoming a father," the source said. "Khloe still has trouble doing it sometimes. She wants to come back to Cleveland, but she does not know what date she is. [going]. The move is postponed for the moment. She seems very unhappy about leaving her family. She had the best summer of L.A. "