Khloé Kardashian wants desperately to return Los Angeles to be with her family, but for now, what's best for newborn daughter True comes first – and that means staying in Cleveland

Khloé Kardashian wants desperately to return Los Angeles to be with her family, but for now, what’s best for newborn daughter True comes first – and that means staying in Cleveland.

A source tells PEOPLE the new mom, 33, is not headed home just yet despite the cheating scandal involving boyfriend Tristan Thompson.

“Yes, she would like to be back home in L.A., but she’s also doing what’s best for her child,” the source tells PEOPLE.

The insider continues, “She wanted to give the baby time to adjust and to literally stay alive, so she’s of course following doctor’s orders.”

Despite staying put in Cleveland where she’s currently living with Thompson, 27, the source adds the Keeping Up with the Kardashians star is still determined to return home.

“The plan is for her to get back to L.A. when they can.”

Credit: Khloe Kardashian/Instagram

For now though, the new mom is focusing on the positives and is over the moon about her new bundle of joy.

“Khloé’s in heaven right now as a new mom,” the insider says. “Drama with Tristan aside, she’s super happy and really trying to enjoy every moment with her baby.

Khloé welcomed her first child with Thompson on Thursday — just days after allegations surfaced that the Cleveland Cavaliers player was unfaithful to the reality star throughout her pregnancy.

The Good American jeans founder was paid a visit by sisters Kourtney Kardashian, Kendall Jenner and Kim Kardashian West, who were spotted flying into Cleveland on Monday. They then flew back to L.A. Tuesday with mom Kris Jenner.

While the KarJenners remain supportive of Khloé, tensions are allegedly simmering between the sisters and Thompson. On Tuesday, a source told PEOPLE that Kim, 37, and her husband Kanye West, 40, were upset with the Cleveland Cavaliers player for his alleged infidelity.

Credit: Khloe Kardashian/Instagram

“They both feel Khloé has gone through so much and that she deserves being happy,” said the source. “They can’t believe that Tristan has been going behind everyone’s back. They find his behavior disgusting.”

“Kim is very protective of Khloé and is especially upset,” the source added. “She can’t imagine Khloé will stay with Tristan but will support her sister either way.”

RELATED VIDEO: Why Khloé Kardashian’s Daughter True Has Tristan Thompson’s Last Name: They’re in This ‘Together’

Thus far, the future of Khloé and Thompson’s relationship remains unclear, and sources have told PEOPLE the new mom is choosing to focus on her newborn.

“Khloé really wants to be able to forgive and trust Tristan again and have the life she hoped to have with him,” one insider told PEOPLE on Monday. “She doesn’t know if she’ll be able to do that, but that’s the goal. She loves the life they had, she loves the baby they have together, and she still loves the dream of being a family together. If she can find a way to rebuild with Tristan, she will.”

And according to the source, the Keeping Up with the Kardashians star never considered giving her daughter her own last name.

“Khloé still very much loves Tristan, and this baby is one half his,” said the source. “True is their child together. Giving the baby his last name was never in question.”