Why do you think that Bovatec is the culprit in your case? Is your horse eatting a feed that is produced in a factory that also produces cattle feeds with Bovatec in them?
Peritonitis is not common in horses and when it is seen is usually caused by some sort of perferation of the GI tract (surgery, truama, bacterial infection, etc) which allows the contents of the GI tract to leak out.
Treatment for peritonitis is generally long-term antibiotics and supportive care (IV fluids, change in diet, anti-inflammatories, etc). If you are concerned that maybe the treatment being offered isn't appropriate/enough or that maybe there needs to be more done diagnostically, consider asking your vet to consult with a vet at one of the teaching hospitals or maybe have a second vet assess your horse.
To help your vet, you need to go back over everything that has occured in the last few weeks--changes in diet (including a new batch of feed or hay), water intake, changes in the quality of the water (newly treated well, change at the water treatment plant, etc), changes in the envirnment (temps, animals in the area, work going on in the area, etc). Make a list of changes and how they coincide with the appearance of symptoms in your horse and have that list available for your vet to look at. History is a very very important part of assessing health conditions.
Licensed Veterinary Technician