Willow and Jaden Smith reportedly "feel bad for their dad" and wish some things "remained private".
The two young stars - whose parents are Will Smith and Jada Pinkett Smith - are said to be wishing some things hadn't made it into the public sphere after their mother made some shocking revelations, including her and Smith’s breakup seven years ago, while promoting her new memoir 'Worthy'.
An insider told 'Entertainment Tonight' that Willow, 22, and Jaden, 25, "feel bad for their dad with all the recent headlines about their parents".
The source added: "They know he has been going through a lot lately and this isn't helping.
"They wish some of their family's private matters remained private."
Meanwhile, the insider said the 55-year-old actor - who also has son Trey Smith with ex-wife Sheree Zampino - is "trying to stay busy and has been hanging out with his good friends and his kids".
They continued: "He's trying not to let any outside noise impact him. Will loves Jada and feels like he has always had her back and always will.
"He has been trying to be supportive, while also taking care of himself."
Pinkett Smith, 52, caused a stir last week when she revealed she and the 'King Richard' actor had secretly been separated for the last seven years, but she's now insisted they are committed to restoring their "life partnership" and are "concentrating on healing".
Speaking on 'Today' on Monday, she said: "We are working very hard at bringing our relationship, yes, bringing our relationship back together... back to a marriage again.
"Husband-wife marriage for me, for my healing process. I came into that with very specific ideas, right? Very specific ideas that were blocks. To me just seeing Will to who he is. He can't be this perfect idealised husband.
"I have to be able to accept him for the human he is. He accepts me for the human that I am, and we want to love each other there."
The 'Red Table Talk' host has also explained she does not live with her estranged husband at the moment but expects to do so again in the future so she can "take care" of him.
She told the Sunday Times magazine: "To be honest with you, I think eventually we will [live together again] I really do.
"Will's getting old. I'm staying quite young, but it's getting apparent to me that he's gonna need someone to take care of him."