Their father, remanded on Wednesday to Pollsmoor Prison as he awaits his bail hearing, was not there.
“It was well attended and the support network is strong," said Juan Smuts, attorney and spokesperson for the children's mother Julia Engelhorn.
Engelhorn found the twins, a boy and a girl, dead at the Princess Beach Road holiday home of her ex-husband Mario Yela, last Thursday afternoon.
In Yela’s first appearance at the Wynberg Magistrate’s Court on Wednesday, State prosecutor Benito Adonis alleged Yela, 48, sent Engelhorn a text message inviting her to join him for lunch and then told her he had killed their twins.
It was reported Adonis said in court Yela told Engelhorn he had killed them when she arrived at the house, where she found the twins dead and Yela with a knife in his hand.
Yela reportedly told her he had dropped their seven-year-old son at school.
Magistrate Momina Ismail remanded Yela to Pollsmoor Prison until a bail hearing scheduled for Wednesday.
Yela’s attorney, William Booth, had requested the defendant be hospitalised for injuries sustained at some point after fleeing the house.
Yela, a Spanish citizen, fled the Princess Beach residence in Engelhorn’s vehicle. Police apprehended him in Wynberg.
Yela spent the weekend at Victoria Hospital under police guard and did not appear in court until Wednesday. Booth told a Wynberg magistrate on Monday his injuries were too serious for him to appear.
Police spokesperson Noloyiso Rwexana would not disclose the nature of the injuries but said the suspect had been injured prior to his arrest and was admitted to hospital immediately after.
Adonis alleged in court on Wednesday they were self-inflicted and minor.
A source told Weekend Argus Yela had suffered “stab wounds”.
The couple had gone through a “complicated” divorce in 2015, Smuts said. Yela had flown in from Europe two weeks ago to exercise visitation rights and was scheduled to fly out of South Africa.
The children had last been with Yela in Spain in December and January.
A postmortem had been done, but the cause of the twins' death had not been disclosed.
“We’re awaiting the results,” Rwexana said.
Booth is among South Africa’s best known defence attorneys. He has previously received threats for defending suspected paedophiles and was a frequent commentator on the sensational Oscar Pistorius trial.
Engelhorn has lived in Spain since 2012.