You made the comment that "as long as sex is safe, it's okay." That's a solid philosophy, but I want to broaden it. Sexual safety is about so much more than appropriate birth control; it also includes emotional attachments, trust, and respect. By those standards, your unease is absolutely justified. Even if the hook-up was consensual but uncomfortable, it left you with the feeling that you may be hurting Dan's wife, a bystander. That makes it feel unsafe. Why have sex if you leave with sickening guilt?
In short, Contact, you absolutely are allowed to "impose" your values onto sexual partners — when it comes to behaving ethically. And here, your standards are straightforward: honesty, openness, and consideration for other people. It seems that these very basic tenets aren't being met. Even in its best-case scenario, this doesn't sound like a group of people who are communicating and looking out for one another. If you are "feeling sick about it," listen to those voices — that means something's not right. A situation that makes you feel like you can't trust your own instincts or that you're "spiraling out of control" is likely not a good one.