I didn't see the Today show and haven't yet read the locked Today Show thread, so excuse me if my theory contradicts what is already known.
I think the emails under discussion may have been sent recently. I wonder if LE has used 1 or more email recipients to "entice" TH into saying ugly things about Kyron and her feelings toward him. I'm not saying she was set up, or that anyone has falsified her remarks in any way. More like LE may have heard hints from various people that TH had a lot of resentment toward Kyron, and then went looking for someone from inside her camp who would be willing to encourage, collect, and turn over evidence of this from Terri, in her own words.
I think LE likely shared the emails with Desiree knowing that Desiree would tell about it in the press, maybe even encouraging her to do that. And the reason would be that they're hoping this will encourage others to come forward and provide more information about Terri's true feelings and behaviors toward Kyron.
One thing that comes to my mind is what Kyron might have told his friends. A kid might not tell his bio mom or dad about a step parent who isn't always as kind--and safe--in private as she was in front of other adults. But kids, I believe, can be more truthful with one another. Kyron might have said more to the kids in his circle if Terri had bullied him, swore at him, said mean, hateful things to him--or even hit him.
I have long felt that it's possible that whatever happened to Kyron happened because he was headed off for a weekend with Desiree and there was a danger he was going to reveal something to Desiree that TH didn't want Desiree to know.
As for LE sharing the hurtful emails with Desiree, I think she probably has an understanding with LE that she wants to know the truth, however hurtful it may be. If I were in her position, I would not want people sparing me, coddling me, hiding things from me. I'd want to know whatever little scrap of true information I could find out about my son, even if it made me cry! When LE showed her the emails, I'm sure there was someone right there with her, and the revelation was no doubt handled as gently as possible.