I agree, out of the 3 #1 is best, but I'm thinking "I help my son with showering" would be better. It might be different in other English speaking countries however.
Number 1 is clearly the best of those choices. However, it is still awkward!
"I help my son take his shower"
One does not take one's shower the way one take's one's dog for a walk. They way #1 is phrased is as if you are carrying the shower away not washing in it.
Avoid redundancy of mentioning your son and the posessive "his", you should really say: