The paper proves an Ulyanov-type inequality for the mixed modulus of smoothness of a generalized Liouville--Weyl derivative of a function of two variables in mixed metrics. The derivative is defined by transforming the two-dimensional Fourier series by a positive general monotone sequence of the class  and by phase parameters. The main estimate relates the mixed modulus of the derivative in the metric  to an integral operator involving a dyadic functional constructed from angular best approximations of the original function and differences of the multiplier. The proof combines the mixed Ulyanov inequality, an inverse estimate of the modulus through angular approximations, and a two-dimensional Abel transformation for multipliers. Particular cases include the classical Weyl derivatives and logarithmically modified multipliers.