Christopher Reeve's children reveal his private world in new documentary (exclusive)

When Christopher Reeve's children Matthew, Alexandra and Will Reeve were still small, their father – who rose to fame in 1978 with his role in the film Superman – was the guy who could do absolutely everything: fly airplanes, sail a yacht, ski, ice skate, ride a horse, play the piano.

He was also a brilliant kid, studying at Cornell University and the Juilliard School. But as much as he seemed like a real hero, it was the way he handled his life after his fall from a horse in 1995, which left him paralyzed from the neck down, that made the biggest impression on his children.

“Heroism is so much more than superficial strength and a glossy image,” his 32-year-old son Will tells PEOPLE about his father's legacy. “It's about integrity, about being there for your family, about persevering in difficult situations and still finding joy in life. That's what our father was like.”

The actor's three children are excited to give an insight into their father's private life before and after the accident in the new documentary Super/Man: The Christopher Reeve Story (produced by Words + Pictures), opens in select theaters on September 21 and again on September 25 (which would have been Reeves' 72nd birthday).

But as much as the film shows how Reeve dealt with adversity and became an activist for the paralyzed community, it does not sugarcoat Reeve's life before the accident.

He was indeed famous and handsome, but he also had his problems. These included a strained relationship with his father, a strict professor who he never seemed to be able to please, and inner turmoil because of the role imposed on him as Superman.

He also ended his relationship with Matthew and Alexandra's mother, British model agent Gae Exton, when the children were young, leaving them heartbroken. The film helped the children better understand their father.

“It’s a wonderful thing to be able to see the bigger picture of a person’s life,” says his daughter Alexandra Reeve Givens, 40, an activist who sits on the board of the Christopher & Dana Reeve Foundation.

She adds: “There were ups and downs, but also two deep true loves and [three] Children who together formed this wonderful family.”

Reeves' eldest son Matthew, 44, a filmmaker whose footage from two previous documentaries he made about his father was used in the new film, also points out that they wanted to tell the full story of his father's life.

“We wanted to honor his story, but not make it a sugar-coated eulogy,” he says, noting that it was also important to show how hard Reeves' life was after the accident, from learning to breathe on his own without a ventilator to the cost and physical toll it took on the actor and his caregivers, including his devoted wife, Dana, who devoted herself to caring for her husband.

Will, who was almost three years old when his father was injured, says of Dana Reeve: “My mother was perhaps the most extraordinary person who ever walked this earth. She had a unique combination of grace and beauty and compassion and courage and intelligence.” All three children agree that Dana was the glue that held the family together after the accident.

The film's directors, Ian Bonhôte and Peter Ettedgui, say that during filming they realized how much Reeve had changed not only physically but also mentally as a result of his injury.

“Christopher learned what was important after that,” says Bonhôte. “He wasn't interested in making a successful film or playing more roles. He was interested in his family and focusing on his close ties.”

Alexandra says: “Our father had a near-death experience and knew he couldn't leave anything unsaid. Since we were suddenly not doing any physical activity, we had a lot more time to sit around in his office and talk. It was a real gift.”

Will adds: “I see Matthew and Alex being phenomenal parents… with my mum and dad shining through them in the best way. You're there for the people you love and you give them everything you've got because you don't know how long you're going to be with them. That's something I took from my childhood and will carry with me for the rest of my life.”

Tickets for Super/Man: The Christopher Reeve Story, Visit Fathom Events.

To read more about the extraordinary life of Christopher Reeve, pick up the latest issue of PEOPLE on newsstands Friday.