You can sue, but honestly it wouldn't be a very strong claim. If insurance has covered the damage, I assume that the hotel would be covered under it as well, so if your only claim is infliction of emotional distress, then it would not be worth filing suit over.
Are they covering the cost to repair her place and the costs incurred as a result of having to live somewhere else? If so, then it is unlikely that there could be additional money for emotional distress. You could sue, but you would probably have a difficult time finding an attorney to take on the case - especially if the stress is the only item of damages remaining.