Spector said that it would be hard to predict how each of the four children, who span a decade in developmental age, will handle the truth of their father's affair.
"It will take a long time to sort this out," she said. "It was the same way with the [John] Edwards children. Of course, they also had to deal with the fact that their mother [Elizabeth Edwards] was dying and is now dead. Their father was the only parent in that role and they had to find forgiveness."
Democratic presidential candidate Edwards has a 3-year-old daughter, Quinn, with Rielle Hunter, a filmmaker he met on the campaign trail in 2007. The truth about his "love child" was kept secret until an investigation by the National Enquirer revealed his infidelity and the financial support he provided for mother and daughter.
His wife, Elizabeth, filed for divorce, although he was at her bedside with their children when she died in December 2010. At the time, their daughter Cate was 28, Emma Clair was 13 and Jack was 11.
The Schwarzenegger children have also lost close family members in the last year. Their grandmother, Eunice Kennedy Shriver, died in August 2010, and their great uncle, Sen. Edward Kennedy, died two weeks later. Their grandfather, onetime vice-presidential candidate Sargent Shriver, died in January after a long battle with Alzheimer's disease.
"The Schwarzenegger-Shriver family were devoted Catholics, so they may forgive and find it within their faith to go on," said Spector. "The support system should be in place. But it's been hard for them and this family has also weathered other well-known affairs --- they have family to talk to."
But psychologist Kazdin said that having a large family -- even the Kennedys -- does not give these children immunity from profound reactions. "A large family has nothing to do with a large support system," he said. "The experience of loneliness is not the number of people in your life."
Research shows that maintaining routines and giving children a loving support system can help them cope during this kind of stress. Other adults, including close relatives, can provide continuity in their lives.
Changes in school, living arrangements, their social network of friends, can make their adjustment even more difficult. Emotional upheaval is associated with changes in the immune system that can make people vulnerable to sickness.
"Try to keep as much routine as possible and the rituals in childrearing to allay anxiety and provide stability in the family," said Kazdin. "It could be as trivial as grocery shopping on Saturday morning."
If their parents can minimize the "direct open conflict" in front of the children, they will fare better, he said.
"Given their prominence, this family could use the media to fire weapons at the other person," said Kazdin. "We have seen this in the news in other custody cases -- using the media to fuel a fire that is already there."
Schwarzenegger and Shriver should also attempt to address questions about the affair openly, "but don't go wild," advised Kazdin, who said there might be slips of anger and resentment.
"We are only human," he said, especially after a betrayal and loss of trust.
As for their newly revealed half-brother, Kazdin said the child likely wasn't close to the Schwarzenegger children.
"My expectation is that they never knew the child was related to them and the mother didn't have him there for sleepovers," he said. "Probably, they had no contact. This will pass pretty quickly and I doubt there will be an emotional bond."
But psychologist Spector disagrees.
"Christopher, now knowing that his father was expecting two children at roughly the same time, albeit under very different circumstances, might feel as if his arrival was somewhat less special than that of his older sibs," she said.
Even though they may have mixed feelings, the Schwarzenegger children must face the reality: "Up until now, he was the son of a person they knew well and presumably liked," she said. "Now, her position in their world is very different but their attachment through their father to this other son means he's a part of their lives in some respect whether they want it or not."
Can there ever be a happy ending for the family?
"Yes, it's possible," said psychologist Spector. "Human beings have a tremendous capacity to change and evolve. There are times when people really do forgive and move, but it's hard and it's rare."