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The majority of binary star systems that host exoplanets will spend the first portion of their lives within a star-forming cluster that may drive dynamical evolution of the binary-planet system. We perform numerical simulations of S-type planets, with masses and orbital architecture analogous to the Solar system’s four gas giants, orbiting within the influence of a $0.5\, \mathrm{M}_{\odot }$ binary companion. The binary-planet system is integrated simultaneously with an embedded stellar cluster environment. ∼10 per cent of our planetary systems are destabilized when perturbations from our cluster environment drive the binary periastron towards the planets. This destabilization occurs despite all of our systems being initialized with binary orbits that would allow stable planets in the absence of the cluster. The planet–planet scattering triggered in our systems typically results in the loss of lower mass planets and the excitement of the eccentricities of surviving higher mass planets. Many of our planetary systems that go unstable also lose their binary companions prior to cluster dispersal and can therefore masquerade as hosts of eccentric exoplanets that have spent their entire histories as isolated stars. The cluster-driven binary orbital evolution in our simulations can also generate planetary systems with misaligned spin–orbit angles. This is typically done as the planetary system precesses as a rigid disc under the influence of an inclined binary, and those systems with the highest spin–orbit angles should often retain their binary companion and possess multiple surviving planets.