However, Glenn had filed for two temporary restraining orders against Kenney in 1994, WBZ-TV reported.
Glenn wrote on one of the orders dated Oct. 9, 1994: "He knows I'm afraid of him and every time I tell him I want him out or I'm going to call the cops, he tells me, 'I'm going to kill you.'"
Glenn had ended her relationship with Kenney and moved from New Hampshire to Lowell about two months ago, according to godmother Lela Boykins Hall.
"She was at the House of Hope because the relationship had ended," Hall said. "She tried to be a good mother to them. She said she left...It was not safe for her children or for her."
Two other women in Massachusetts, one in Brockton and the other in Everett, had current restraining orders against Kenney.
Kenney had been convicted previously for other crimes.
He had several outstanding warrants for crimes including cocaine possession, receiving stolen property and motor vehicle violations, Davis said.
Glenn had been staying with her children at the House of Hope, shelter for homeless families a few blocks away from the scene of the shooting.
Glenn had been living at the shelter for three or four weeks, another resident of the shelter said.
The Associated Press contributed to this report.