Answer: Unfortunately, based on your description I can't picture the area with any great certainty, but one way to keep the stones in place without interfering with the water might be to layer wire mesh over them and pin that to the soil. However, in general water problems worsen over time rather than improve (and in many areas it is illegal for a neighbor to direct water at your property). Odds are good that this problem will not be solved in the long term by adding edging. I would suggest you have a professional drainage expert take a look at the area and make some suggestions.
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