Katherine Schwarzenegger tweet
"I love my family till death do us apart," Patrick Arnold Schwarzenegger, 17, tweeted.
He also quoted lyrics to a song by hip-hop group Fort Minor that read "some days you want to quit and just be normal for a bit."
Big sister Katherine Eunice Schwarzenegger, 21, also tweeted (as KSchwarzenegger), "This is definitely not easy but I appreciate your love and support as i begin to heal and move forward in life. I will always love my family!"
They are two of the four kids that Shriver and Schwarznegger have together.
Earlier, Shriver appealed for compassion and privacy in breaking her silence on her estranged husband's admission.
"This is a painful and heartbreaking time," Shriver said in a statement. "As a mother, my concern is for the children. I ask for compassion, respect and privacy as my children and I try to rebuild our lives and heal. I will have no further comment."
The Los Angeles Times reported overnight that the former California governor admitted to Shriver that he'd fathered a child with the woman, who had worked for the family for 20 years.
Schwarzenegger's admission to fathering a child with a household staff member resulted in his separation from wife Shriver, 55, according to the Los Angeles Times.