You can't block your AH's e-mail (I have the same issue as you do with the kids), but you can block your MIL's. You have no reason to interact with her.
What has helped me a lot is typing up e-mails as if I used e-mail like my mom does, for conveying important information only. You'd think she's military the way her e-mails only focus on the necessary. That's how I write AXH now:
"I'm not able to take the kids that weekend.
DD has a dentist appointment on Monday at 2."
Etc.
It helps to set the tone that way, I've found with my AXH.