Multiple submission of same work for different audiences
This is actually something my group also deals with extensively. A lot of the work we do is focused on improving existing computational methods to improve their efficiency or extend their range. A lot of the time, the actual work done is of very little interest to the end-user audience, but quite significant from a computer science perspective. So a lot of our recent work has been divided in exactly the manner you propose: we present the basics of the method and some end-user applications in papers geared toward the application community, and specialized papers for the methodology that are directed toward the CS community.

The main thing to remember is that the publications should stand independently of one another as much as possible. Some overlap will of course be inevitable here, but you should strive to make the "stories" they tell as distinct as possible.