Autumn, while I'm generally in favor of NO CONTACT unless it's something involving the kids, I also don't think there's anything wrong with OCCASIONALLY dropping a little "truth dart" on them:
H: I know I made some bad choices, and I regret them more than imaginable and wish I could prove how sorry I am. I just want to make things right moving forward with you.
Autumn: Talk is cheap, (Husband). You have broken so many promises to me already. Only consistent actions -- over time -- will mean anything. For your own sake, and for the kids, I do pray that you can pull it off, despite what's happened with our marriage.