It's an interesting question. I myself would feel very uncomfortable in your situation, so I will try to think out loud about why.

First, out of curiosity, do you think this is a relationship which would work if the wife knew about it? That is, if being a mistress serves a reasonable, niche purpose and does not really threaten your boyfriend's life with his family, why do you think our society is typically so quick to get angry at mistresses, and why do so many wives feel unhappy and threatened by them?

Or is there, perhaps, really something about the asymmetric information (you know everything and keep secrets, while secrets are kept from his family) which makes the situation work for you, makes it exciting and pleasurable? If this is the case, presumably it is important for you to feel that there are no secrets between you and him.  Would it bother you if you found out by accident that recently your boyfriend has taken another mistress as well, and that she knew about both you and the wife, whereas you did not know about her? It seems to me that to accept the position of secret mistress, one has to believe that to withhold information about a relationship (say, from the wife) is not an unforgiveable betrayal of trust. However, the few people I have known in this situation found it all very difficult to accept being cheated on, even when they themselves were a mistress. Or is your situation and philosophy different from what I have described?

I don't mean to judge your choices, this is also an emotional issue. Admittedly, monogamy is complicated.

You make some good points.

There are perhaps a couple of missing pieces to my story. 

On my part: I was married once, gave my all to it, and it turned out to be a terrible, terrible experience.  I swore I would never give another person that much power over my feelings again.

On his part, he is from a rather conservative religious background which embraces the idea that a wife is always a nagging bitch.  She lives up to the part.  Because of the stigma within his community for himself and his children should the marriage end, he will never leave. 

Were we people with different kinds of baggage, then either I would say forget it or he would get divorced, but as it is, the arrangement serves both of our needs.  We both get companionship, support, sex, and a best friend without me losing my freedom or him losing his standing among friends and relatives.

If he took another mistress, I would be furious. 

Essentially, I am his emotional wife while his "wife" is the business partner with whom he provides structure and care for his young children. 

My only child, by the way, is a young adult and fully aware of the situation.  The two of them get along quite well.  He taught her how to drive, and she often works for him when he needs extra help at his office.

It is a crazy world we live in.