"He was not perfect — far from it," Ted Kennedy, Jr. said of his father. "But my father believed in redemption and he never surrendered, never stopped trying to right wrongs, either as a result of his own failings or ours."
His father, Ted said, will be remembered as the "workhorse of the Senate" and a "beacon of social justice." Patrick Kennedy noted that he and his father co-wrote legislation to provide health insurance coverage for those suffering from mental illness.
CBSNews.com's complete coverage of Sen. Edward M. Kennedy's life and death
"My dad was never bowed, he never gave up, and there was never quit in dad," Patrick said.
The brothers ruminated on Sen. Kennedy's ability to work with those who disagreed with him.
"He even taught me some of life's harder lessons -- such as how to like Republicans," Ted said to laughter. "He once told me, he said, 'Teddy, Republicans love this country just as much as I do.'"
Patrick said his father's approach to politics was similar to the way he approached his other life passions, such as boat racing.
"I saw a lot of his political philosophy in those races," he said. "One thing that I noticed on the boat, as in this country, there was a role for everybody, a place for everybody to contribute."
Along with sailing, Sen. Kennedy had a zeal for a number of activities from painting to skiing to rodeo riding, the brothers said. He was recruited to join the Greenbay Packers footbal team as a young man but decided to go to law school instead.
One of the greatest lessons he passed on, Ted said, was to never give up. He shared the story of how, when he was 12 years old, his father helped him climb an icy hill, even though Ted, Jr. had lost a leg to cancer.
"He held me around my waist, and we slowly made it to the top," he said. "He said, 'I know you can do it. We're going to climb that hill together if it takes us all day... And I knew I was going to be OK...He taught me that nothing is impossible."
Read more stories on Sen. Kennedy's life and death at CBSNews.com:
Obama: Kennedy Was "The Greatest Legislator of Our Time"
Mass Honors "the Greatest Legislator"
Barack Obama's Eulogy for Ted Kennedy
Locals Share in Mourning of Kennedy
Photos: A Final Farewell
Photos: Funeral Honors Kennedy's Legacy