Sounds like you want to watch a couple of circle packing tut’s.
Like this perhaps…
Or look at the Demo Files on the blender site. Try the Simulation > Index Of Nearest file.
I assume this logic can be applied to the curves either of the snakes, or the curves they are following. If you can get the radius at a position the simulation should be able to keep that distance between.
A simpler method may be to activate the Curve: Extra Objects Add-on, and add a few knot curves for the snakes to follow.