Your life should not be dictated by your husband's perceptions of you. Know what? The reality is that divorced people don't send their XW e-mails to read to the kids and expect a response. You pick up the phone and you call them. Your life is not on hold waiting for his next call and e-mail. If it were me, I would stay so busy that I didn't even check my e-mail more than 3-4 days a week and I'd only respond to half of them. That's life. If he has a problem with that...just tell him you've been busy.
As Ian said, you are too worried about what he's thinking or what impact your actions have on him, rather than focusing solely on yourself and your own growth. He's a fully functional adult....if/when he wants to be part of your life, he'll make it clear. If not...still his problem. Take ownership of what you can control.
You cannot be lonely if you like the person you're alone with. Dr. Wayne Dyer