In order to solve dynamic problems of double non-identical quantum harmonic oscillators with interaction potential and movement coupling, the new two mode composite coordinate representation |η1，η2〉 is proposed by the technique of integration within an ordered product of operators. The two mode squeezing operator U is constructed, and its characteristics are analyzed. Moreover, its application to double non-identical quantum harmonic oscillators with interaction potential and movement coupling is presented for solving some the dynamic problems. Approach of solving some the dynamic problems involving complicated quantum harmonic oscillators is proposed.