What was your agreement regarding dating other people while you are separated?
Assuming that it's NOT agreed to, I would say to her:
"I am NOT okay with you having an affair while we are still married, make no mistake. It's incredibly disrespectful to me and our marriage, and it needs to stop."
If she says you're controlling, say "that's not the issue -- the issue is your affair." If she denies the affair, put your hand up (as in "STOP") and say, firmly, "Stop it. Please stop lying to me -- it's very disrespectful."
If she says "we're just friends," say "First of all, we BOTH know that's not true, but even if it were, you'd be putting a friendship AHEAD of your husband, and that's not right. If the situation were reversed, I would honor your wishes."
Most people on these boards are not advocates of "snooping," but I think good intel-gathering has its purposes. Legal/strategic/tactical aside, it would help you muster up the strength you need to set a firm boundary and enforce it. With your wife separated from you physically now, that will be harder to do, but there are still ways you can gather more intel to find out more accurately what you're dealing with.
