Just continue being the loving husband and father that you are. Don't pretend like you don't hear her. When she said those things, respond to her ("I can print it out", "Your mother is right, you need to be in bed", etc.) Your kids love both of you and don't want to take sides. She wants them to act like you don't exist. It's ridiculous.
That's good about talking to them. If they want to talk to you, they will. SOunds like you are ready when they are and that's all you need to do.