In the end it's their property - you can't move onto a property with poor fencing and expect that to improve just because you are paying board.
As for the water, it depends. An empty water trough does not necessarily equal neglect - is it ALWAYS empty? Or was it just that one time? It's summer after all, and sometimes they just go through water faster than we can keep up.
The property owners being home doesn't mean that they have nothing better to do than fix fences and fill waters immediately as required. In the end, your board money isn't enough of a motivator to change how they manage their property.
If you want more done, you either need to move (which doesn't appear to be an option) or start doing these things yourself. The catch to having the extreme luck of having horses at your age is that you are at the mercy of your parents in situations like this. If you don't see eye to eye on horse care, then unless you can find a way to make it work it may be easier on your conscience to hold off on horse ownership until you can call the shots.