Marissa Rodriguez insisted her husband Juan would never do anything to hurt the children.
The 39-year-old is accused of leaving the twins in the car after he forgot to drop them at daycare.
It is believed the children died while sitting in the vehicle as it baked in 30C in the Bronx, New York.
Meanwhile, their dad went to work at a veterans’ hospital.
His wife has said she will “never get over” the children’s deaths, but insisted her hubby is a “good person”.
“I blanked out. My babies are dead. I killed my babies”
In a statement to NBC, she said: “I will never get over this loss and I know he will never forgive himself for this mistake.
“This was a horrific accident, and I need him by my side to go through this together.
“Though I am hurting more than I ever imagined possible, I still love my husband.
“He is a good person and great father and I know he would’ve never done anything to hurt our children intentionally.”
Rodriguez, an Iraq War veteran, sobbed when he appeared in court to plead not guilty to manslaughter and homicide.
He told police at the scene: “I assumed I dropped them off at day care before I went to work.
“I blanked out. My babies are dead. I killed my babies.”
Neighbours described him as a doting dad who had just recently set up a bouncy castle in his garden to celebrate the twins’ birthdays.
Juan and Marissa – who also have a four-year-old – wept outside Bronx Criminal Court after posting $100,000 bond on Saturday.
He is accused of leaving the two children in the backseat of his Honda Accord for eight hours – with their bodies reaching 42C.
The veteran returned to his car at 4pm, drove for 10 minutes, and then realised the babies were in the backseat.
He screamed as he saw the children “foaming at the mouth”, attracted the attention of a passer-by and called 911.
One neighbour said: “He was always doing things with the kids. Always in the yard playing
“They had a big camp-out last weekend, with tents in the backyard. He would always play catch or basketball with his older kid.”
Around 50 family members showed up at court to support him as he was hailed before a judge on Saturday.
“This is a tragedy of horrific proportions,” Rodriguez’s defense lawyer Joey Jackson told the judge as his client wept.