You have listed a few unrelated issues. First the water issue. I wonder what benefit does the tenant have by "faking" water issues. Just because a plumbing issue isn't there today doesn't mean it won't be there tomorrow. Maybe the shower drain became loose as a result of handling the plumbing from the tub issue. Maybe it was there at the same time but wasn't discovered. Maybe the plumber just guessed at the cause and it has nothing to do with plumbing.
Water flows in the easiest path it can find. I once had a water problem that formed in the ceiling and wall of a living room. It was finally discovered that external water was coming from a rotted attic vent over twelve feet away. The water was running along the wall's interior framing, and there was no exterior evidence until the water pooled in the upper corner of the living room and continued down the wall.
You mentioned reported wetness after a rain. This should concern you. Okay, you and a friend tried to inspect and re-create the problem using a hose. But if your not watering the exact problem area, your efforts are futile. You may have a leak problem other than, or in addition to, a plumbing problem. I suggest having a contractor take a look to find the culprit of the leak before it becomes a much larger, costlier problem.
Onto the carpet. Damage to your property as a result of the tenants and/or their pet(s), the repair is the tenant's expense. If you decide to seam the carpet to repair the damaged area from the water, that's a cost effective choice. If you replace the carpet, are you going to let the tenant pick it out too? I'm sure any tenant would be interested in buying the property they rent if the landlord replaces, updates, everything within the home before buying.
The ex-husband. It sounds as though the tenant has violated the lease by allowing the ex-husband to live on the property as a tenant. You have a few options. One, ignore it, but not my first choice. Two, have the ex-husband provide an application with appropriate fees, run the application so you know who is living on your property, and add the ex-husband to the lease. Three, enforce that the ex-husband vacate the premises or evict the tenants for violating the lease, although if you know the ex-husband has been there for 2 years or more and evicting now may cause an issue during the eviction.
I highly suggest you get the water issue professionally looked at, someone other than a plumber, or in addition to, as it may not be a plumbing problem. Repair the carpet or replace it. Decide whether or not the tenants are good tenants and worth keeping. Determine if you want to add the ex-husband to the lease or evict them for violating the lease. At the end of the day all the decisions are yours to make.
Managing rental properties is tough, it’s time-consuming, and often comes at a considerable cost in terms of stress and heartache. If you’re not getting satisfaction providing hands-on management, you may also want to consider hiring a professional property manager.