In an at-home interview marking her May 10 graduation with top honors from Rollins College, Nordegren tells PEOPLE that things are "really good" between her and her ex, who live just a 25-minute drive apart in southern Florida and see each other regularly as they share custody of daughter Sam, 6, and son Charlie, 5.
"I have moved on and I am in a good place," Nordegren says. "My relationship with Tiger is centered around our children and we are doing really good – we really are – and I am so happy that is the case. He is a great father."
Though devastated when Woods's double life as a serial cheater – with at least a dozen women – unspooled in late 2009, Nordegren says that as a child of divorced parents herself, she never doubted that she and Woods would eventually find equilibrium. A psychology student, she went through intensive therapy at the time of the split and still checks in with her therapist every week to keep "working on myself."
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"In the beginning, you tamp down the animosity for the kids' sake," she says. "I'm not going to deny that I went through the wringer. But I don't think I doubted we'd end up here. That was always my dream, that the kids can have two loving parents that show respect for each other. And I feel that's what they have."
For much more of PEOPLE's interview – including a peek inside Nordegren's gorgeous new home, new romance and new plans for her future – pick up the new issue of PEOPLE, on newsstands Friday