I would surprised if the defense didn't try to get the confession tossed. But, he also made the confession "I did it" as he was being arrested up in Gordon. So, IMO he had two distinct admissions of guilt and I believe that is going to be impossible honestly IMO.
LE has 'boxes of evidence" as per their statement. The gun used to kill JC & DC, the car and physical evidence gathered from it, ie Jayme in the trunk, etc.
I agree having to have Jayme testify would be horrible and traumatic, but if it put the murderer of her dearly loved parents behind bars for LWOP, I believe she'd rise up again and be able to stand for them.
JMO