No, don't email her. It's pursuing.
I've been following your thread, because I am in a bit of a similar situation, not knowing whether to blow the cover off my h's affair -- he's lied to his family, to me, to everyone, pretending that he's just a long suffering sad boy in a miserable marriagee (boo-hoo) and nothing about the 4 affairs in the past ten years.

I digress, sorry.

You have been given great advice here, mb. If your h is coming over tonight, why would you hang around doing homework? At the very least, clear out and go to the library to do the work. He doesn't need to know that.