The purpose of the Epsom Salt is to contract the gallbladder, increase the peristaltic activity of the bowels and purge the stomach. It has a purpose in the Hulda Clark e liver flush. Without the Epsom Salts then its another protocol. It isn't strictly used as laxative in the conventional sense. It is stop the bile being reabsorbed in the sigma colon, expel any toxic bile quickly and prevent a blockage in the cut.
If you struggle with it then the first step is to adjust the dose. One tablespoon is more than enough for many but other can tolerate twice that amount. Try reducing the amount of Epsom Salts until it just produces runny stools.
Here is my link to an article about Epsom Salts and it's role in the liver flush.