Sluss is accused of murdering the Holly Springs mother, who was reported missing in July. He faced a judge in Wake County Thursday.
"We're definitely feeling relieved that that day has finally come," said Melanie Tucker, Moynan's mom.
"Just a huge relief to know that he was finally going to be behind bars," said Brandon Tucker, Moynan's stepdad.
"I was relieved, broke down, had this whole resurfacing of everything that we're continuing to go through knowing that now we're entering this completely new phase," said sister Samantha Moynan.
That next phase is the legal process. Sluss was arrested in Virginia and extradited to North Carolina, appearing before a magistrate Wednesday.
READ MORE: Ex-boyfriend accused of murdering Holly Springs mom Monica Moynan extradited to Wake County
Moynan's family called her 'Moni.' They're remembering her as a great mother, friend and family member. They said she had just signed up for classes to become a doula. But she never made it to those classes.
"She would light up a room, had a great energy, great vibe, great sense of humor," Brandon Tucker said.
Her family still wants her body to be found.
"It is super important to my heart," mother Melanie Tucker said, getting emotional. "She's my child, my baby. I gave birth to her and took care of her and loved her and was there for her for her entire life."
"She deserves to be at rest and our family deserves to know where she is so that we can honor her in that way," Samantha Moynan said.
"We need to be able to know that she's not out there alone," Melanie Tucker said. "We just need to be able to bring her home."
As for a possible motive, Melanie Tucker said:
"I think that she came to the realization that she could break free of him. She was doing that. She was definitely doing that. And I think he sensed that this was the one time that he wasn't going to be able to reel her back in."
Sluss has a court-appointed attorney. His next court date is June 11.