A time-dependent Kondo model in the Toulouse limit is considered as follows: the oscillations in the voltage with frequency \Omega and in the coupling parameters with frequency \Omega/p (p\in\mathbb{N}). A non-perturbative technique is proposed, namely, the non-equilibrium Green's functions and physical observables are averaged over a period of 2\pi p/\Omega. When only the voltage oscillates, one sees the Kondo satellites as stated in the previous studies. Moreover, the features of the differential conductance and magnetic susceptibility become richer when the Kondo couplings are considered oscillating on time. We obtain the satellite peak splitting. Our results show that the distance between peaks, which appear in the differential conductance -- magnetic amplitude characteristics G\left(H\right) or in the differential conductance -- dc voltage characteristics G\left(V_{dc}\right), can be smaller than \hbar\Omega.