Good luck, you can of course search for all algorithms ... but IMHO thats fairly intuitive.

A convex hull should be easily computed incrementally by adding one atom after the other to the former convex hull.

Of course you need the bases in vector algebra like multiplication with normal vector of a plane to find the direction (inside or outside).

And I think you can already restrict yourself to calculate the convex hull of the atoms within the intersection of the spheres to gain speed.

UPDATE: In other words: If there are any separating planes, then there is for sure one which is a margin of the atoms in the sphere intersection.