Hi, I am Savannah Breeze. Depending on how many horses you have on your 1.5 acre property, there may be a few things to try. It sounds like you might be keeping your horse in a 1.5 acre dry lot. This size area would put out a lot of dust and manure fumes into the air. Cross fencing your pasture (dividing it into 2 to 4 smaller paddocks) might give you an opportunity to start some grass growing in 2 or 3 of those paddocks, while you keep your horse in the smaller space for a period of time (on hay obviously). These smaller areas will also be easier to manage (keep free of manure). Then, as your grass has a chance to grow, you can rotate the horse through each of the other paddocks for several days at a time. This will help to keep grass cover on the ground and help reduce the dust issue.
Meanwhile, to help break up the manure that has not been removed from the paddock you might try dragging a couple of tires behind you using a sit down mower or small vehicle, driving directly over the manure piles to spread them out. This will spread and break apart the manure allowing it to dry more quickly. Once it's had a chance to dry thoroughly, this should reduce or eliminate the odor and will help reduce the number of flies. For loose matter on the ground (dust), you might try having someone come in to blade the ground (scrape off the top dusty surface). Also, you could spray the small dry paddock with water once or twice a day to minimize the dust.
Finally, since this sounds like your situation might be getting a little serious, you might want to contact the local Natural Resources Conservation Service or Cooperative Extension to get some advise on how to resolve some of these issues quickly. If they can't help you they may know who can. Last but not least, if you haven't yet done so, try talking to your neighbor, tell them how much this horse means to you and that you're trying your best to address his concerns. This may be able to buy you some time to try some of the above.