The custody stuff is the big deal, of course. Sounds like you are making reasonable requests, and I hope she goes for it.
The apology/affidavit is emotionally appealing to you, I understand (having been in your shoes), but it ain't worth a hill of beans. Your X won't admit she lied, because in her mind she didn't, or at least, she can always "plausibly deny" (you can thank Pres. Reagan for that phrase) that she lied. And even if she did sign something like that, it doesn't preclude her from anything in the future, at least that she can again plausibly deny. So, if you can get it from her, it means nothing; and if it detracts from the big picture, then you are hurting yourself.
Otherwise, good luck.