The ongoing custody battle between Rob Kardashian and Blac Chyna has continued … and gotten so much nastier.

Chyna says that Dream isn’t safe at Rob’s because she got burned with him, but he says that Dream’s had a lot more injuries at her mom’s house.

TMZ reports that Blac Chyna is trying to insinuate that Dream Kardashian is unsafe under Rob’s care.

Allegedly, Dream received not one but two burns while at her father’s house.

Chyna got the Los Angeles Department of Children and Family Services involved — always a correct move when a child’s safety is in question.

Though Rob initially denied that the second burn happened under his care, he has blamed Dream’s former nanny for the alleged negligence.

Now, Rob’s attorney Marty Singer has confirmed that Dream ended up getting burned in two incidents …. both times with the former nanny.

(Those of us who spent thousands of hours of our lives caring for younger siblings without them getting burned probably have questions for that nanny)

Singer expressed confidence that social workers will not find anything unsafe or otherwise out of line in Rob’s home.

He also says that Rob treated the incidents appropriately and also filled in Blac Chyna on what had happened.

Singer also opined that it is “unfortunate that Chyna feels the need to publicly miscommunicate the situation.”

He suggested that she “has once again wasted valuable public resources by calling first responders in a desperate attempt to smear Rob’s name.”

Singer claimed that Chyna did this “in response to his ongoing lawsuit against her for full custody of their daughter.”

Things then took a turn for the worse when Singer expressed concerns about Dream’s safety while she spends time with her mother.

According to what Singer told TMZ, “third parties” have sent DCFS to Chyna’s home over worries about Dream’s treatment and safety.

Dream has allegedly come back from spending time with Chyna with “many” unexplained injuries.

According to Rob’s team, that has included “rashes, cuts, bruises, and a dislocated arm.”

While that’s not an explicit accusation of abuse, it seems to be implied, and the situation sounds extremely serious and dangerous for the 3-year-old.

At present, both Rob and Chyna share joint legal custody and physical custody of sweet little Dream.

They are both hoping to snag primary custody — and, at this point, we wouldn’t be surprised if either of them demanded sole custody.

Previously, Rob — backed up by Khloe — has claimed that Dream’s behavior has changed for the worse after spending time with Chyna.

She has allegedly been more aggressive immediately after being with her mom, and apparently even hit one of her cousins shortly after a visit.

One of the difficulties in assessing the safety, whether in terms of neglect or abuse, of children Dream’s age is … they are very prone to injuries.

Three-year-old Dream has obviously not been walking for all that long, and her body is growing every day.

In short, preschool agers like precious little Dream are extremely clumsy because they are new to the world, and can fall or bump into things.

But as we all know, they can also be easy targets for abuse from frustrated caregivers. They are helpless and fragile.

Blac Chyna has a history of well-documented volatile behavior, including her very public throwdown at Legoland.

Rob is a first-time parent who has had his own struggles. Either of them could be making serious mistakes.

The best solution may be to have Dream under the constant supervision of a team of nannies — the same nannies at either parent’s house.

Those nannies could then answer to, say, Khloe or Kris or to the court itself, rather than to the parents.

But we don’t live in a world that prioritzes the safety of children over the “rights” of their parents, so we can only guess what will come of this.

View Slideshow: Dream Kardashian Photos: What a Cutie!