I would pull her out in a second for the smoke. That is a definite deal breaker for me regardless of sacrifices or hardships that it would cause. I hate cigarette smoke and won't tolerate it in any form around my children.
The other 2 issues aren't as severe for me. The diaper rash would bug me and I would talk to the provider about it. I know that providers have several kids in their care and can understand how a diaper wouldn't be changed immediately. If it was severe then I would probably pull her out for it. I would casually bring the bad thing up to the provider. She could have heard the word anywhere and it could have been something that just stuck with her.
I really like a pp's idea about finding a teenage girl to be a mommys helper after school! Good luck with the situation!