The transition phenomenon of few-cycle-pulse optical solitons from a pure modified Korteweg-de Vries (mKdV) to a pure sine-Gordon regime can be described by the non-autonomous mKdV-sinh-Gordon equation with time-dependent coefficients. Based on the Bell polynomials, Hirota method and symbolic computation, bilinear forms and soliton solutions for this equation are obtained. Backlund transformations (BTs) in both the binary Bell polynomial and bilinear forms are obtained. By virtue of the BTs and Ablowitz-Kaup-Newell-Segur system, Lax pair and infinitely many conservation laws for this equation are derived as well.