Michael Jackson's three children, Prince Michael I, 12; Paris, 11; and Prince Michael II ("Blanket"), 7, have been trying to gain a sense of normalcy since their father's death in June. With the support of their grandmother and guardian Katherine Jackson, the children are "slowly coping."

One source tells PEOPLE 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]," says 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."