A source tells PEOPLE the family's "primary concern is protecting Dream from all this nastiness"

Rob Kardashian‘s famous family is not pleased with him after his explosive social media rampage against his ex Blac Chyna on Wednesday.

While Kris Jenner and her daughters have remained noticeably silent about the drama on social media, a source close to the family tells PEOPLE the stars are “deeply disappointed and frustrated with Rob.”

“He’s made a difficult situation even worse,” adds the source of the news, which is just the latest flare-up in Kardashian and Chyna’s roller coaster relationship, which first began in January 2016.

As for whether the family is worried that Kardashian could be subject to criminal charges for sharing explicit photos of Chyna on social media, the source says they’re focused on Kardashian and Chyna’s daughter Dream Renée, 34 weeks.

“At this stage, the primary concern is protecting Dream from all this nastiness,” says the source.

It remains unclear who is currently taking care of Dream, though on Wednesday evening, Kardashian, 30, took to Snapchat to share a photo of his daughter in the bath.

Credit: Rob Kardashian/Snapchat

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On Wednesday, Kardashian’s Instagram page was shut down hours after he repeatedly posted graphic and expletive-ridden content about Chyna, in which he accused her of drug use, alcohol abuse and infidelity, sharing three alleged nude photos of her.

After his Instagram account was disabled, Kardashian took to Twitter to continue his rampage, alleging that Chyna only had a child with him to get back at Kylie Jenner and Tyga. (Chyna has a notoriously complicated history with the Kardashian-Jenner family: She was previously engaged to and shares a 4-year-old son with Tyga, 27, who went on to date Kylie, 19, on and off for almost three years. The two have since split.)

“Loved Chyna as my wife and accepted all the wrong she did and continued to ride for her and remain Loyal to her,” tweeted Kardashian on Wednesday. “Never did I cheat.”

“But she couldn’t remain loyal and cheated and f—ed way too many people and she got caught and now this is all happening and it’s sad,” he wrote. “We had a beautiful baby girl that was the best thing that’s happened to me and soon as that baby was born Chyna was out.”

“Soon as kylie and tyga broke up Chyna was over the game. She had a baby out of spite and I’ll never view her the same,” he continued. “I truly thought Chyna wanted to be a family and that’s why I was so loyal to her but I learned my lesson and everyone else was right.”

Chyna, 29, initially responded to the onslaught of messages in a Snapchat post, alleging that Kardashian hit her. The Snapchat was then taken down, and neither Kardashian nor Chyna have responded to PEOPLE’s requests for comment.

Chyna’s attorney, however, told PEOPLE on Wednesday he is “exploring all legal remedies and protections available” in order to “best advise her on how she may want to proceed.”