If convicted of either charge, Wall could spend up to life in prison.
Defense attorney Fred Metos remained confident that Wall would see a reduction in bail from another judge because, the attorney told reporters after the hearing, his client is no threat to society and is willing to wear a GPS ankle monitor to ensure he does not flee the state. They plan to ask for a $100,000 bail.
"In this country, a person is presumed innocent until proven guilty," Metos said. "Dr. Wall has no history of violence and has been cooperative throughout this two-year investigation."
The couple's 19-year-old son planned to testify Monday that his father is a violent, vindictive man who poses a threat to himself and his four children and should not be allowed to make bail. But he declined to speak when it became clear that bail would not be addressed at the hearing.
After, he told a group of reporters gathered in the courthouse hallway that he was glad his father remains in jail.
"We're very happy that he's still in jail and that his bond has not been reduced," Pelle Wall said.
The son recently commissioned a psychological profile of his father that describes the doctor as an angry, selfish man who "would sacrifice any member of the family for his own needs."
The report was written by Richard D. Walter, a private consulting psychologist from Pennsylvania who specializes in criminal profiling.
Friends and family of the victim have said they long thought Wall capable of harming other members of his family. Pelle Wall, who believes his father murdered his mother, has also fought for custody of his three younger siblings on the basis that their father might harm them.
"There are two people in there," said Heidi Schubert, who worked with von Schwedler at the university. "There's the person who's a pediatrician who can take care of people's children, and then there's the person who's full of anger and rage and could kill someone else."
Uta Von Schwedler, 49, drowned in the bathtub of her Sugar House home on Sept. 27, 2011.
For months, authorities struggled to determine whether the woman's death was murder or suicide.
But expert analysis of the crime scene has revealed a violent struggle and Wall's DNA in the home, which he did not share with his ex-wife, according to charging documents.
Von Schwedler and John Wall had a contentious divorce in 2006 that led to years of custody battles over their four children, which prosecutors have cited as a motive for murder.
But Metos has said Wall had been prevailing in the custody struggle and had no reason to hurt his ex-wife.
Von Schwedler was found dead in an overflowing bathtub of ice-cold water by her boyfriend, Nils Abramson. A scrapbook was lying on top of her and a knife was later found under her body. Blood was found in her bedroom, at the edge of the bathroom sink and on a window sill, charging documents state.
She was practically naked, wearing only shorts, and had cuts on her left wrist and leg and injury to her throat, as well as a potentially lethal dose of the anti-anxiety medication Xanax in her system, for which von Schwedler did not have a prescription, according to an autopsy report.
Charges allege Wall had written and filled a prescription for his mother for 30 Xanax tablets in May 2011, though there was no documentation indicating he was treating his mother medically.
Pelle Wall, the couple's eldest son, has attracted the attention of local and national media for his outspoken position that his father is guilty of murder.
In April 2012, Pelle Wall filed a petition in 3rd District Juvenile Court aimed at removing his three younger siblings from their father's custody. In June, the court and family reached an agreement that removed the children then ages 16, 13 and 11 from John Wall's home.
In December, the son filed a wrongful death lawsuit against his father.
But two months later, the younger children were returned to John Wall by Juvenile Judge Charles Behrens. Since their father's arrest, the children have been staying with relatives.
Metos said that should the doctor be released from jail, the children would likely stay in the care of their eldest brother and the relatives who have taken them in since their father's arrest.
At Monday's hearing, von Schwedler's friends and family packed the courtroom gallery wearing rainbow stickers proclaiming "Justice for Uta."
They wanted to make their presence known to the court and lend their support to the von Schwedler family, Schubert said.
"He's a danger to the people Uta cared about," she said. "We just want to make sure he stays behind bars. That's what matters."
Wall will next appear in court in June.