Dyeing is the most time and energy-consuming process in textile production. Motivated by a dyeing overdue problem in a lace textile factory, we study a parallel machine scheduling problem with different colour families, sequence-dependent setup times, and machine eligibility restriction. An integer programming model is formulated to minimise the total tardiness. Given that the dyeing optimisation problem is strongly NP-hard, a hybrid differential evolution (HDE) algorithm embedded with chaos theory and two local search algorithms is proposed to solve real-world instances from the textile factory. In our proposed algorithm, a special encoding and decoding scheme is designed to deal with the machine eligibility constraint, and chaos theory is adopted to determine the parameter settings of the underlying differential evolution (DE) algorithm. To speed up convergence and improve search exploitation, two local search algorithms inspired by two dominance properties are developed to determine the optimal job sequence for parallel machines, such that the decision of the entire problem is simplified to the assignment of jobs among the machines, and the computational time required is significantly reduced. Comprehensive experiments based on 36 synthetically generated small to large-scale problem instances and 20 real-world industrial data sets confirm the efficacy of our proposed HDE over other DE variants.