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We experimentally investigate the dependence of the fragmentation behavior of the ethylene dication on the intensity and duration of the laser pulses that initiate the fragmentation dynamics by strong-field double ionization. Using coincidence momentum imaging for the detection of ionic fragments, we disentangle the different contributions of ionization from lower-valence orbitals and field-driven excitation dynamics to the population of certain dissociative excited ionic states that are connected to one of several possible fragmentation pathways towards a given set of fragment ions. We find that the excitation probability to a particular excited state and therewith the outcome of the fragmentation reaction strongly depend on the parameters of the laser pulse. This, in turn, opens up new possibilities for controlling the outcome of fragmentation reactions of polyatomic molecules in that it may allow one to selectively enhance or suppress individual fragmentation channels, which was not possible in previous attempts of controlling fragmentation processes of polyatomic molecules with strong laser fields.