Here is the sentence again:
With sharp scissors, Thinh tried to even her client's hair, but the woman
kept twisting in her seat to yell at her two small children who were terrorizing
the salon, Thinh finally decided that crooked
ends were better than poking out a client's eye.
The woman kept twisting in her seat to yell at her two small children ... is a main clause. Thinh finally decided ... is the second main clause. Joining these two is a comma alone, which creates a comma splice, a major error in sentence structure.
If you put a period after salon instead of the comma, you would fix the problem.