I wanted to tell you what I know about mother snakes:
For one thing, boas and others (as you said above, adders) bear live young. Pythons and colubreds lay eggs and incubate them.
Female pythons lay the eggs and then they coil around them to incubate them until they hatch. Then they leave, they do not stick around the mother the young. But while incubating they coil around the eggs, and adjust themselves to keep the temperature and humidity of the eggs (the two most important factors to hatching the eggs) just right. They loosen it tighten coils to release or keep the humidity generated by the eggs. Some species bask to warm up then return to the eggs but many types of pythons will contract all of the muscles to make a "shivering" type motion around the eggs to warm them.
The mothers are perfectly designed to lay and hatch the eggs and are good mothers for that, they act as they need to in order to breed healthy young. They are fire/action oriented in that way. But reptiles do not, as far as anyone can tell, and I've kept snakes for over 20 years, have any emotions. They do what is right, and they certainly have physical responses to stimulae, the definitely feel pain and warmth and cold and seek closed, safe places to rest (or high branches, etc depending on the type) but they do not have the part of the brain that feels emotions. They definitely act on instinct, 100%! This seems a very wand-like quality to me.
I wonder if these ideas help anyone in their views of this image. I love it personally!
Eta: snakes do not have emotions, so they're not water/cups, they aren't intelligent so they're not swords/air, I could see where we might think pents/earth because they are associated with the medical cadeusis we often see. In fact, the original Greek symbol for medicine was the Rod of Asclepius, one snake around a rod (a symbol of the god Asclepius, associated with the healing arts and medicine).
The caduceus is a rod topped with wings and wrapped by 2 snakes - a symbol of the Greek god Hermes - therefore it can represent commerce/negotiations/messengers, but also of alchemy - the Universal Solvent, Azoth (a universal medication sought in alchemy - the word azoth is derived from the word Mercury. It is also, alchemically, the essential agent of transformation (I see wands/fire here!). The association with Mercury is with fire. Levi wrote that azoth is the source of enthusiasm and activity of the Alchemist, it is industry, physical labour. Azoth = the elixir of life/ the philosopher's stone, the animating spirit of life itself.