I take it you're on a well system and not city water?
Is your sprinkler system powered by the well water pump or is there a booster pump on the sprinkler system?
Is your sprinkler system "down hill" from the home?
It sounds to me like something in your sprinkler system is causing a pressure drop so severe that its almost, or is, a vacuum at your hot water tank. This could happen if you had an over-sized sprinkler pump drawing too much water from the home supply, or if you had sprinkler outlets located horizontally well below the home.. (think house on a big hill).
Another issue could just be that your well pump is not even close to big enough to power both the home system and the sprinklers and maybe there's less pressure drop through the sprinklers than the home plumbing system and so that's where the water goes.
One other thought... If you have a water filter installed for the home, it could be plugged and since the sprinklers probably by-pass the filter, the large pressure drop in the home causes the lack of water and it goes to the sprinklers.