They were stabbed to death.
A federal judge in New York sided with prosecutors who argued that the financier poses a flight risk.
Shkreli was sentenced to seven years in prison last year for his conviction on charges he looted a drug company he founded.
The 31-year-old suspect and his wife and children shared the house with the mother and children who were killed, authorities said.
The Berkshire District Attorney's Office announced Wednesday that remains found in Peru, Massachusetts have been identified as Jackie Coutinho, a mother who disappeared from Hinsdale in May of 2019. Coutinho was a resident of Florida.