The Menendez family is blaming the Los Angeles District Attorney's Office for the hospitalization of Terry Baralt -- Erik and Lyle's aunt ... claiming the graphic crime scene photos they were shown did a number on her health.

In a press release from the Justice for Erik and Lyle Coalition -- a collective of family members fighting for the brothers' release -- the group confirmed our story that Baralt had been found unresponsive in her hotel room.

The coalition says the D.A.'s office didn't give the family a heads up that they would be presenting photos of the crime scene at Friday's resentencing hearing ... a violation of Marsy's Law, a law designed to protect the victims of crimes.

The moved showed "no humanity – just shock and pain inflicted on people who have already endured decades of grief. Terry, who is battling cancer, came to court to support her family. No physical pain has ever kept her from being there for her nephews. But the display put on by the DA’s office pushed her past the brink. By early this morning, she was rushed to the hospital and remains in critical condition."

The Justice for Erik and Lyle Coalition this most recent move was deliberate, completely ignoring Marsy's Law ... and also feeds into a "a disturbing pattern we’ve come to expect, especially from D.A. Hochman, who has repeatedly spoken to us with aggression and disdain and we will be holding him accountable."

The coalition finished off its statement by adding, "Our family is hurting. Terry may not recover from what was done to her – and to all of us – in that courtroom. We deserve better. We firmly believe that if the DA’s office had shown even an announce of consideration for us, as victims, we would not be hoping for one more day with Terry right now.”

Bryan Freedman -- a famous attorney who serves as counsel for the victim's family members -- echoed the statement, telling TMZ ... "I was appalled that without so much as a warning to allow them the option to avoid further distress, the D.A. callously decided to re-traumatize the family by needlessly showing insensitive photos on screen in their court presentation.

"This despicable action was a clear violation of Marsy’s law which requires absolute empathy toward victims. The D.A.’s flashing of the crime scene photos is directly responsible for Aunt Terry being rushed to the ICU. We are all praying for her recovery, she did not deserve this. Shame on those who knowingly engaged in this egregious conduct."

As we told you ... the resentencing hearing is set to take place next week -- with the brothers' attorney Mark Geragos -- who cohosts our "2 Angry Men" podcast -- calling on a judge to change Erik and Lyle's first-degree murder sentence to a manslaughter sentence, for which they've served enough years for immediate release.

Gergaos blasted the D.A's use of the graphic crime scene photos Friday too BTW ... calling the choice a "dog-and-pony show" -- and adding they are "being traumatized by the D.A. for political purposes."