Is it acceptable to ask a client to cover cleaning costs?

I empathize and have experienced some of this too, even when offering dogs walks every couple hours and being with them all the time. I haven't asked any client to cover cleaning costs and basically it seems like the expectation is that dogs will just do this and sitters will have to deal with it, like you have by giving frequent outings, restricting space, and trying diapers or belly bands. Rover's Terms of Service even states a Pet Care Service Provider is not entitled to reimbursement for damages to their property caused by pets in their care.

What I'd suggest is just nicely letting them know what's going on and hoping that they may offer a solution and maybe if you're very lucky some reimbursement.

I think what you're probably seeing is a combination of stress, an avoidance of rain, and potty training that hasn't been generalized to all indoor spaces. Any incontinence issues the older dog has will likely be worse when under a bit of stress, but it's definitely worth telling the owners what you're seeing. If it's not normal for him to have incontinence at all, it may be indicative of a bigger problem that they should check out. If it is an issue normally and is just worse when he's stressed, there are medications that their vet can prescribe to help. Management for both dogs (supervision, containment, helping them relax) will be your best bet for this current visit.

Dogs are very good at learning new things, but not great at generalizing concepts. What this means is that anything they learn is very situational. If you teach a dog to sit, they first learn that the cue "sit" means "put my butt on the floor... when I'm in this room, when you're holding a treat, when you're facing this way, when you say it in this voice, etc..." It takes many training sessions in many environments with many variables and distractions before a dog learns that "sit" ALWAYS means "sit," regardless of where they are or what's going on around them. For most simple cues, we do this almost subconsciously even if we aren't familiar with how dogs learn. But for the most part we don't do a lot of potty training away from home unless we spend a lot of time with our dogs in a variety of places. As a result, a lot of dogs are house trained in a few places where they spend a lot of time, but haven't done a lot of work training in new places with a variety of floor types or people, and especially not in places where a high volume of dogs come through leaving their unfamiliar scents behind like a sitter's home.

Finally, dogs learn best by learning what TO do rather than what not to do, so in any new setting, showing them where you want them to relieve themselves will be your quickest mode of success. Always take guests out to the same place for potty breaks, and when you do get one of them to potty outside (which might take a lot of time if they're hesitant to go in the rain), be sure to give them over the top praise, treats, toys--whatever lets them know that you love what they did. This is a good practice for every guest, even if they haven't had any accidents, since prevention is far better than reaction.

You could write off the cost on your taxes, it is a business expense. I would NEVER ask a customer for money and I wouldn't take those dog in the future. I get a lot of dogs that are potty trained that still poop and pee in the house. Being left in a new place is stressful for a pup. I removed my carpet and buy cheap throw rugs now. Happy sitting, Amber G.