@Andrew3557
I agree with you that 10% of one nights accommodation is basically nothing for an essential amenity. I would ask to speak to a supervisor as the rep handling the claim is not being helpful.
Please make sure:
1) All communication was on the airbnb app or platform as to document your case. Keep track of your case number and the rep assigned to your case. If you call in to speak to another rep, reference your case number for continuity so all notes can be kept in the same place and the rep can see what has been going on.
2) Take detailed notes as to when you notified the host, when they responded, and how it negatively impacted your stay, comfort, especially being that you were tracking with kids and water was not running and it an essential amenity, no toilet facilities, no showering available, etc. spell out everything.
3) Read the Airbnb terms of agreement regarding amenities advertised and what was provided. Regardless if it was an accident that the water tank went dry, it was not as promised, so a compensation (more than 10%) should be granted. To my knowledge they can grant up to 30% for every night there is missing a major amenity or something disruptive happens during your stay.
4) Keep on following up with different agents, supervisors, etc mentioning your case number.
Focus on how it negatively impacted the following: your vacation, your stress levels, your impression of the Airbnb as you expected a better experience in the handling of your concern, the inconvenience of unsanitary conditions (toilets not working for 3 days is not sanitary - did the host come to provide a camp toilet or water for washing dishes, hands, etc?), and that if not handled in a amenable manner you will be sure to let people know about your experience.
I am sure if you are persistent you will have a better response and please do ask to speak to their supervisor if you are not getting anywhere with the reps.