I don’t read it as her “taking him back” as much as her committing to move on and not allow her anger or bitterness poison the lives of her children and herself.
Well, perhaps I'm misreading it...it sounded to me that she was a bit too eager to let him off the hook before he was completely "cured" of the sin of betraying her with his love for another woman (stated, essentially, just yesterday)/
Personally I take it as a political move on her part. What is the sense of putting this stuff out publicly. She could have sent him a letter, called him on a private line, done anything except make this even more public than it has been. I also read it as you do, that she is not willing to take him back, just forgive him, but since she says it in a press conference she has an ulterior motive, one that has little to do with her marriage, except to use it as political gain.