Relative position using Accelerometer
What you heard (about double integration and accumulating errors) is correct. Mathematically, you can do this, by integrating each device's acceleration to get its current speed, and integrating the speed to get it's current position, then taking the vector difference in the their positions to get the distance between them.

If you had highly accurate accelerometers in a very noise-free environment (both mechanical and electrical noise), you could do it for a (short) while before the inevitable tiny errors (which are also being integrated!) begin to dominate the data and make the results useless. But as a practical matter - especially for us experimenters using inexpensive equipment and subject to a lot of mechanical and electrical noises on the experimental platform, plus environmental electrical noise - this will happen even more quickly.