Suspect Amanda Hayes has filed motions saying she has an alibi in the murder.
When neither of the Hayes' attorneys objected to a joint trial in March, the judge ruled their trial would start May 20.
However, the judge said the arraignment could change during the trial if one of the defendants should offer evidence the other feels is damaging to their case.
If that were to happen, the judge would have to decide which defendant would continue to be tried and which would be tried later.
Ackerson's remains were found in Oyster Creek near Skinner Lane in Richmond, Texas July 2011. Identification was made through dental records days later. The 27-year-old was reported missing on July 18.
Texas deputies said they believed Ackerson was killed in North Carolina, and then dismembered, before her body was taken to Texas in coolers. The creek where the remains were found is near Amanda Hayes' sister's home.
During a 2011 court hearing, an assistant district attorney told a judge that Grant Hayes wanted Ackerson out of his life. Ackerson and Hayes had been involved in a custody battle over their children for more than a year. Hayes was later granted primary custody in 2010.
Grant Hayes was a local musician in Raleigh.
Prosecutors said he legally changed the spelling of his last name from Hayes to Haze, so they now refer to him as "Grant Haze, a.k.a. Grant Hayes."