There are many sections under which you can file civil and criminal cases for your husband having s*xual relationship but in reality you cannot get a judgment in your favor. For s*xual conduct, as pointed above, you will need actual evidence of them having intercourse or extremely compromising position without clothes...Actually these days every husband is looking out for some s*x outside marriage. Some get it some don't. You husband seems to be a lucky guy. Don't torture yourself unnecessarily. You too have options... Think beyond law.
In practice, you have two options. One is to take divorce as you suggested yourself. Second is for you to find someone to have s*xual relationship with and enjoy life because clearly your husband does not want you or has found someone better for s*x. That physical urge is God given and is too powerful to be stopped by legal proceedings. So? You do the same but make sure that there is no evidence anywhere. Try and avoid cheap hotels. They may have hidden cameras there. Change your partner and hotel frequently so that the likelyhood of getting caught is less. After a couple of months or so, you will enjoy this lifestyle and will not care about your husband's affair. No need for divorce or DV... Both of you will need to change partners, say once in six month, to live happily ever after... And yes... do not forget, Try to have married partners. There are no legal hangovers in such arrangments and no emotional, love-shove issues. I hope that you find this suggestion helpful.