The bodies of 47-year-old Debra Denison and her grandsons, 2-year-old Alton Perry and 6-month-old Ashton Perry, were found Tuesday night in a car parked near Lake of Isles in Preston, in the southeastern part of the state.
State police called the deaths a double murder-suicide Wednesday, saying they believe Denison shot the boys and herself. Autopsies were planned.
Family members said Denison had bipolar disorder and a history of mental health problems.
Tuesday was Alton's second birthday. Denison picked up the children from their daycare in North Stonington Tuesday afternoon and was supposed to bring them home so Alton could open his presents, family members said.
"I wanted him to come home and play with his new toys and have a good day," Alton's mother, Brenda Perry, told WVIT-TV.
In Facebook postings late Tuesday and Wednesday morning, Brenda Perry thanked people for their prayers and said she loved her sons.
"God (has) two beautiful angels helping him now," the postings said. "My boys are in an amazing place we got a few great angels watching over us. love you Ashton and alton."
On Monday she wrote: "So excited making mini cupcakes and play dough for Altons day tomorrow can't believe 2 years old already. So blessed"
Perry and her husband, Jeremy, told WVIT that Denison had a gun and suffered from split personalities.
A man who answered the door at the couple's home on Wednesday declined to comment to an Associated Press reporter.
Denison was armed with a gun when she left her home Tuesday afternoon and had permission to pick up the boys from daycare, state police spokesman Lt. J. Paul Vance said.
A phone message seeking comment was left Wednesday at the daycare, Kidds & Co. A posting on the daycare's Facebook page said, "Our love and prayers are with the Perry family. Tomorrow (Wednesday) will be difficult for all of us but we are here to offer our support to all our families and staff."
The bodies were found at about 9:30 p.m. Tuesday, about two hours after state police issued a statewide Amber Alert for Denison and the boys.
Denison had two convictions for minor driving offenses, said Peggy Muckle, a clerk at New London Superior Court. She was fined $35 in 2003 for following too closely and, in 2004, she pleaded guilty to reckless driving but a judge did not require her to pay the $100 fine.
Associated Press writer Dave Collins contributed to this report from Hartford, Conn.