I don't know how a person "stumbles across" another person's email. That sounds like snooping to me. In an ideal world, we could talk to our partners about our needs and deeds and desires without turning into secret agents. It sounds like a terrible way to find out about an affair: both because you were lied to and because (it sounds like) you violated her privacy.
The point I'm trying to make is that you need to work on communication. You can't be expected not to become jealous if you feel you're getting tricked. But you'll have to invest some trust too if you want her to be honest with you about how she's feeling (and what she's doing). The same goes for you. You need to be able to talk about these feelings with her. To do that, first own your own feelings. Take responsibility for your feelings of jealousy and understand where they come from.
I would feel jealous too if a partner of mine had cheated on me, and, yes, there is such a thing as cheating in some non-monogamous relationships. If you negotiate an agreement based on mutual emotional needs and it is dishonestly violated, that's cheating in my book. You should discuss the parameters of the relationship you wish to have with your partner.
As for the loneliness, might I suggest a hobby? If nothing else, having a regular hobby to do will get you out of the house and might even help you meet other like-minded non-monogamists. Try bowling. Or, for the nerdier person, Dungeons and Dragons at the local comic book store can be very fulfilling.
To appreciate your partner's NRE, it helps to feel some yourself. Doesn't have to be a romantic relationship. A new friend (or a renewed old friend) can be very good for the heart.