If you use their computer and their network, they have the right to snoop. Court decisions have sided with the employers. It may not be right but it is.
If you’re a salaried, exempt employee, you ALREADY get paid for working at home on your “own” time. You’re paid for getting the job done, no matter how long it takes. If you’re non-exempt, you are entitled to pay for the time you work, even if it is at home, even if you work at home without “permission”.
What you do with the company’s property, even to access your personal e-mails, is not private. I don’t have anything that’s so important that I have to check my personal e-mail during work hours, and if it was that important, I’d have e-mail sent to my work, in which case it wouldn’t be private.
In any case, our company has blocked access to personal e-mail accounts from work, so it’s a moot point for me.
But nothing you do at work is private. I don’t have a problem with that, and I am able to confine anything I wouldn’t want the company to know about to my non-working hours and non-company property.