We have investigated the spatiotemporal properties of solitons generated on the shallow water surface over a background of a large-scale mode in a hydrodynamic resonator when it is forced near the second frequency mode. We have used the space-time diagrams to highlight the spatiotemporal dynamics of nonlinear fields for two solitons colliding in a resonator and compared them to those of solitons occurring in an unbounded system. A state diagram of experimentally observed modes for different values of the excitation parameters has been obtained. In particular, we have evidenced period doubling and the multistability of nonlinear waves excited in the resonator. For a theoretical description of these experimental results, we have developed a phenomenological model, which leads to amplitude and phase equations of a soliton propagating over the background of a harmonic wave. To reproduce experimental results on the multistability, we have supplemented our analysis with a numerical simulation of a modified system of Boussinesq equations for shallow water, taking into account the dissipation effect