An Alaska judge last week denied Bristol Palin's request to keep the legal proceedings of her custody dispute with Levi Johnston closed.
Palin, 18, filed a petition in early November seeking sole custody of her son, Tripp, and child support payments. She had argued that the scrutiny the case could attract would turn it into a "media circus" that potentially could cause her son embarrassment as he grows older.
"In this day and age of the internet, media stories remain available for years, even decades, after they are first published, and anything printed in the media (whether it is true or not) will be available to Tripp when he is old enough to read," she said in an affidavit.
Levi Johnston, who is seeking joint custody, has pushed for open court proceedings, saying he "just wants a simple case on the merits."
"I do not feel protected against Sarah Palin in a closed proceeding," Johnston said in an affidavit. "I hope that if it is open she will stay out of it. Bristol's attorney is her attorney."
Bristol Palin said that her mother, who resigned as Alaska governor in July, would not be involved in the case other than as "grandmother."
Palin's petition also seeks a visitation schedule for Johnston, who she says has exercised "sporadic visitation rights."
Relations between the Palins and Johnston and his family have frequently been strained since the couple broke off their engagement after their son was born in late December 2008.
On "The Early Show" Wednesday, legal analyst Jack Ford and psychotherapist Robi Ludwig discussed the impact of the ruling and gave a preview of the custody battle ahead:
Johnston denies in court documents that he has avoided his responsibilities.
Sarah Palin announced her daughter's pregnancy days after being named the running mate of Republican presidential candidate John McCain.
Bristol Palin's custody petition calls Johnston's recent nude photo shoot with Playgirl magazine "risque."
The document also notes that Levi's mother, Sherry Johnston, should not be allowed unsupervised visits with the baby following her drug arrest. Sherry Johnston, who is serving out most of her three-year sentence under home confinement, was sentenced last month on a guilty plea to one count of possession with intent to deliver the painkiller OxyContin.
Palin's custody petition also suggested Levi Johnston may have his own issues with substance abuse, saying he made statements about seeking "weed" on Twitter.
Johnston denies making such a statement, saying the Twitter account "is a fraud" and that he doesn't have an account on the popular online social networking site.
In a motion opposing closed proceedings, Levi Johnston's attorney, Rex Butler, argued that Bristol Palin had not shown what sort of evidence could stigmatize the child.
"This case presents a custody case with similar facts that attend open cases every day in the Alaska court system," Butler wrote.