"They're doing great, thanks to the love and support they've gotten," Adam Streisand, an attorney for their grandmother and guardian Katherine Jackson, told PEOPLE in an interview before Murray's surrender.

Seconds longtime family friend Kathy Hilton, "They're getting along and they have an incredible family."

Since their father's death last summer, the children have been living at Katherine's Encino, Calif., estate with cousins and other relatives, growing in maturity and confidence as they play with friends and go on outings -- now without wearing masks and free of the chaos that once followed their father.

"With the kids running around the house, laughing, playing, they've given each other a lot of joy," said Streisand.

Seeking a Normal Life

The trio's older cousins, who joined Prince and Paris on stage at the Grammys Jan. 31 when they accepted their father's Lifetime Achievement Award (shy Blanket was deemed "too young" to take the stage that night, says Streisand), have become mentors to Michael's kids, who remain a tight-knit group.

Helping Katherine raise the kids is their nanny Grace Rwaramba, who had stopped working for Michael before his death but returned afterward upon Katherine's request. Some Jackson family members don't support Rwaramba's involvement, but a source said, "Katherine's made it very clear that it's important to her that Grace is around. She knows the kids are more important to her than anything."

Katherine and Rwaramba are working to ensure that Michael's kids lead as normal a life as possible. "Nothing over-the-top happens" at home, says a family source. Instead, there are school lessons (they are tutored at the house), iChatting sessions and family dinners.

The children go to karate lessons, the library and church. And even though Katherine may be strict (Prince and Paris had to go behind her back to attended the New Moon premiere last November, said a source), she is also giving them room to grow. "Katherine really listens to the kids," said Streisand. "She wants to give them a sense of freedom when she can. She wants to encourage them."

Building Confidence

Being normal also means a lot less spectacle. When the children venture out in public, their faces are no longer concealed. "They like not wearing the masks," the family source said of the trio. "It's a different experience for them."

Another source noted that Prince and Paris have become more confident over the past several months. "It would have been hard to imagine them going out in public or showing up at someone's house hanging out and playing video games before [their father died]," said the source. "That had a lot to do with Michael, because every time he showed up there were bodyguards and [chaos]. And now, not so much. It feels much more normal and they've adjusted really well to that."

And yet, their father's influence lives on.

"Talking to Prince is like talking to Michael," said the family source. "He's so smart and mature -- way beyond his age." Paris, meanwhile, "wants to be a singer."

Adds grandfather Joe, "I was so proud of my grandchildren [at the Grammys]. But I'm always proud of them."