Superior Court Judge Robert Perry told jurors to disregard the story.
Stern, Dr. Khristine Eroshevich and Dr. Sandeep Kapoor have pleaded not guilty to drug conspiracy charges, including providing excessive opiates and sedatives to an addict. The three are not accused of causing Smith's death.
But Alexis testified about one traumatic event after another, including the overdose death of her older son Daniel, saying that three days after his death he still had not been buried.
The former nanny said that cause Smith to take sedatives, become groggy and fall into a pool and nearly drown.
Alexis testified that the next day Smith took medication that Erosovich had brought.
Using a Creole translator, she told the court that Smith was crying.
"She took the whole bottle and she drank the whole thing," Alexis said. "In a second after she drank everything, she fell asleep."
Alexis went on to describe Stern crying and pleading to Smith's limp body. She said Howard shook her to wake up and asked Smith if she wanted to die and if she wanted him to go to jail.
Alexis and her sister-in-law said that when Smith was not taking meds, she could walk without falling, talk and hold her baby. But those were also the times she argued with Stern.
Alexis is a Haitian immigrant living in the Bahamas without immigration papers.
Often confused by the questions, she told the court that she was afraid to testify and at one point was threatened by a Bahamian police officer. Under defense questioning, she said she forgot his name and that there was no witness.
The Associated Press contributed to this report.