Prove adultery

Avail the services of a detective agency, with their help you could get some evidences.

But whats the point, one proving adultery conclusively is difficult and two morally/ethically there is nothing wrong in what your husband did. You are the one who has thrown/restrianed him from entering the shared household and having conjugal relationship, its natural to look for a partner when you have denied him the services that a wife should not have done to a husband. 

Sit with him and try to find a amicable solution. If you talk to him, he might agree for a mutual consent divorce. Why do you want to win a contested divorce when both of you are not happy with each other and which might take a decade of your time? 

good reply stalker

why should always a men be at fault if a lady has not been emotionally able to give a man then she should not expect physical loyality