No. I most likely would not do any pet sitting period. If someone has a cat I might be willing to stop by their place to feed it and remove waste from the litter box once or twice a day assuming they live close by. Dogs on the other hand require walking and want more attention. My house would be off limits either way. Hopefully your family and friends pay you for watching their pets!
Boarding facilities exist to take care of problems like this. I wonder if they feel like their dog is too fragile to handle the boarding experience, or they just do not want to pay for it. (If they think their dog cannot handle the experience, they can pay for a home boarding facility or pay to have someone take care of the dog in their own home.) But would I continue to watch a dog that is not even housetrained?