Thanks for all the blunt feedback. I was thinking it was not a good idea, but just wasn't sure if I was being pessimistic. Kept remembering all the people I knew that were caretakers in Colorado with dogs. We'll have to save pet sitting for when DD can have the dog. Thanks everyone!
Don't take the feedback that it can't work. As I said in my first response, it will just dramatically limit your options.
What you've received are all the reasons why the people responding wouldn't want you to house/pet-sit for us with your dog, but there are people out there who won't hold the same reservations.
I made my reply about dogs fighting because you also need to be aware of that. Even if someone is willing to have you and your dog in their home, are you comfortable with breaking up a vicious dog fight? Handling vet emergencies? Handling the home owners if you ever need to explain to them that their loving, precious, gentle little Bowser who has never hurt a fly actually tried to kill your dog? Because it can so easily happen.
If you want to try it, are able to find clients who are cool with it, and you are experienced and confident with dog conflict (and handling dog owners), then go nuts. If I were in your shoes, I would do it, but I have a ton of experience handling the above. Know what you are comfortable with and act accordingly.