I think that as long as you notify your neighbor exactly when this fumigation is happening and that the recommendation is that she and her dogs should consider other lodging for a couple of days, I think you are ok legally. However, from a good neighbor standpoint, you ought to try to work with your neighbor. Perhaps offer to help with dog kennel fees or a hotel room for her and her dogs.
You and the fumigation company if damage is done to her property, including her dogs. Hopefully you have up to date renters insurance to protect you in the event of a claim. Her dogs will need to be kept away from the poisonous fumes., Perhaps you could agree to pay for all or part of the cost of boarding the dogs for the 2 days in question. That would certainly be cheaper than defending a lawsuit.
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There is no legal mechanism by which you can stop someone from suing you. So, yes, she can sue. It does not mean she will win. You may want to give her any literature that the fumigation company has given you about the precautions to take and any side effects. Animals are considered personal property under the law, so if her dogs get harmed (hopefully that won't happen) or die (breathing in two days of fumigation is not good), she can recover the value of the dog/reduction of value of the dog and any associated bills. She can not recover emotional distress of pain and suffering for her or the dogs. California has one very narrow exception, but it does not apply in your case. Again, that's if she wins. Anyone can sue anyone. Winning is another story. I'm really upset she's willing to leave her dogs there during the fumigation--she is an irresponsible dog owner. Just cover yourself with documents and witnesses that you gave her warning and information. I agree with my colleagues that if a claim is made, you should tender it to your insurance.
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