IMO, this is a really bad idea. I assume you'd want to give him this to get him on your side (though I'm sure you wouldn't call it that; maybe to show him that you're truly changing so he'll speak favorably of you to W, but same thing).
If you sent this, he might take it to heart and speak on your behalf, or he might ignore it, who knows. But even if it were the former, there's no guarantee that your W would listen, and probably a good chance that, regardless, she'd be p*ssed at you for involving her family.
I think you'd be taking a huge risk for very little chance of success.
Listen, MMan, I know you're feeling rushed, you're still panicking a bit at this early stage, and patience isn't your strongest suit at the moment. But no matter how fast W wants to push this, there's no short-cut to doing the work you need to do, nothing you can do to help the journey she needs to make to find her way back to you if she's going to.
Please think long and hard about this letter thing.
