Originally Posted by tinyliny
Is it legal for them to discharge a firearm in their backyard?
Tiny, while it may not strictly be "legal" per say, in most rural areas of the US, those types of laws are not enforced unless the shooter is truly putting someone in danger...like shooting toward town or toward a busy highway without a proper berm behind their target, etc.
Unfortunately, OP, there is likely not much you can do. If they are shooting on their own property and they are not at risk of actually shooting anyone (like the reasons I mentioned above), then the most you can do is report it to law enforcement and watch nothing happen except maybe
the cops might
talk to them.
As for the speeding around your horses, you can do the same and report it to the cops. If they have anyone with time to spare, they may have an officer drive the road occasionally to check for speeders, but the odds that they would catch the neighbors speeding or driving recklessly are rather slim.
IMHO, your best bet for any kind of solution would be to go to their house, ask to speak to them, and then state your position in a mature and well thought out manner. Try to work with them to see if you can come to some kind of agreement.
If they don't have any interest in trying to be reasonable and work with you, then the best thing you can do is watch out for yourself, avoid them at all costs, and simply try not to put yourself in a situation where you have to ride your horse when they are driving or outside messing around.