"They're focused on making sure she is going to be alright," says a source close to the situation.
The 23-year-old singer, who called 911 after she took 8 Traumeel pills, a homeopathic medication, and had trouble breathing, "has the most attentive parents," says a family friend. "She is very close to Billy, and Alexa and her mother are really best friends."
In fact, Brinkley raced from her home in Long Island as soon as she heard the news about Alexa. "She rushed to her daughter's side," says the friend. "She was worried sick. She showered her with affection like she always does. She told she would support her, like she always has."
Since the incident – which was triggered by her rocky relationship with ex-boyfriend Jimmy Riot – Joel and Brinkley have been making sure their daughter knows how much everyone cares about her.
"Alexa is the sweetest girl. She is one of the dearest souls on Earth," says the friend. "She's an artist and like all artists, she's very passionate. Growing up is hard enough to do, but doing it in a fishbowl is unbelievably difficult."
Still, friends are certain she'll be back to her bubbly self very soon. "I have no doubt she will recover fully from this and be horrified that it became such a spectacle," says friend Gail Worley.
For more about Alexa Ray Joel, pick up the new copy of PEOPLE, on newsstands Friday
Reporting by K.C. BAKER and SHARON COTLIAR