Forgiving him depends on a lot of factors. If he is truly remorseful and willing to work on the relationship, it might be possible. But it won't be easy and will take time.
If you've caught your husband in such a situation, first, take some time to calm down. It's a very shocking discovery. You could consider having an open and honest conversation with him about why he did it, your feelings, and what it means for your relationship.
No, it is not a common expression at all. In normal English usage, we don't come across such a phrase. It seems rather strange and not part of the standard vocabulary or expressions.
Well, 'drunk husband loves cock stories' is a rather puzzling statement. 'Drunk husband' is a common enough concept. But 'cock stories' is quite strange. It might be that in some sort of very specific context, like in a group of people with their own unique jargon, it could mean that the drunk man likes stories that are perhaps inappropriate or it could be a completely innocent misnomer for some other type of story. For example, it could be a play on words gone wrong and the real meaning was something like 'clock stories' where the drunk husband likes stories about clocks.
There is no evidence to suggest that such activities occur in a gym environment. Gyms have rules and ethics in place to maintain a proper and respectful atmosphere for all members. This kind of description violates the basic norms of a public fitness place.