Tea, I'm in a very similar situation. The difference is that when my wife wanted to stop having sex, I told her I took that as meaning I can have sex with other women, because being a nonsexual person is NOT an option for me. I suggested we could divorce, but she didn't want to. So I let it be her choice, with the consequences spelled out beforehand. And my choice is also to stay in the marriage because we have many positive other aspects to our marriage.
So far the positives have outweighed the negatives, but I'm not entirely happy with the limitations of friends with benefits. I miss having the old-fashioned kind of romantic sex within a marriage, in our bedroom, in my own home, with the mother of my children, not to mention the security, safety, convenience and social acceptance of the traditional arrangement. I miss the integrated feelings of love and sex all being facets of the same thing, or so it seemed long ago when that was my love life. I envy couples where they seem to have all the sex they want within their own relationship. I've lost the perspective of what that's like.
I'm not recommending my situation to anyone, as I think it's highly dependent on both partners and the compromises they are willing to make. But Tea, my question to you is, have you brought this up with your wife in any way? It's one thing to tell your spouse that you're not going to have sex with them anymore. Like you say, anybody has the right to refuse to have sex. But it's quite another to demand that another person not have sex with anyone! And that's where I've drawn the line. But hey, at least we busted the divorce, and we're both getting what we want sexually.