Nonlinear interactions in wave-group focusing are regarded as one of the main mechanisms in the generation of destructive extreme waves. In real seas, the wideband bimodal state is a typical configuration, containing interactions within a single wave group and between different wave groups. The former has been well uncovered under the assumption of narrow bandwidth, but the latter is poorly understood. In this paper, physical experiments are conducted to reveal the physics of double-wave-group focusing considering various energy distributions. Superposed wavemaker signals generated by the iteration method are applied to produce a double-wave-group focusing with the interactions being decomposed. Results of the wavelet-based bicoherence spectrum show that double-wave-group focusing is distinguished from the linear superposition of two single-wave-group focusing mainly in the nonlinear interactions induced by the second-order sum harmonics. Under the assumption of equivalent energy, interactions of the second-order sum harmonics between the lower frequency group and higher frequency group cannot be ignored in swell-dominated states, and lesser linear interactions and stronger nonlinear interactions are observed while the spectral distribution of the double-wave-group is more asymmetrical. This work is anticipated to contribute to the understanding of the generation mechanism of extreme waves driven by strong nonlinearity.