Maybe engage a PI to follow him if you really think he's having an affair. But d you are not looking at a divorce than perhaps maybe you have to try to make the marriage work. Get him to do some counselling ? Or attend marriage workshop?
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Did you often visit his workplace? Can you visit his workplace? One of the common affair is from the work place. Give him a surprise visit? Especially when he say he need to OT at workplace.
I agree with R Gosh. Women instinct are somewhat always right. You should hire a private investigator if you can't do it on your own.
For me, I will see it with my eyes than I believe.. Mans are the same.. They will deny.. Maybe if you afraid..