The threesomes bring up a question in my mind. Does your wife understand that you don't just want sex? Threesomes can be a lot of fun, but they are no substitute for romantic relationships.
By what you say of the rules and your wife not wanting you to explore on your own, it sounds like she may have some insecurities that are being brought into the light by this turn of events. There's nothing unusual about that, everyone has insecurities of some sort. But maybe getting to the root of those insecurities might help her come to terms with her fears about you dating other women.
Maybe you can help her identify what she's worried about. Is she afraid that you're really just looking for someone to replace her with? Is she afraid to give up her precious time with you? These are just a couple random possibilities, I suspect she's got her own reasons.
I don't need labels to define me. They're sticky and I hate the glue they leave behind.