Multi-scale modelling of damage, fracture, and failure with approaches based on computational homogenisation remains limited by unresolved challenges. One of these issues is the emergence of mesh-dependent effects across spatial scales due to the presence of strain-softening and localisation. This study investigates the attenuation of mesh-dependency in multi-scale computational-homogenisation-based models, including the role of the RVE (Representative Volume Element) length and the combined effects of micro- and macro-scale softening. To that end, numerical examples of multi-scale strain softening are presented, considering porous RVEs to mimic the failure mechanisms of ductile materials. A constitutive model for finite strain elastoplasticity is adopted, together with a simple damage evolution law. Second-order homogenisation reduces macro mesh-dependency and prevents spurious deformations, due to the introduction of a macroscopic intrinsic length-scale. This length-scale is intimately related to the RVE length and evolves throughout the deformation path. Its role in the resulting second-order multi-scale predictions is carefully assessed. The bounds for utilising the RVE length as a numerical parameter controlling macro-scale localisation and softening are thoroughly analysed. Moreover, the second-order multi-scale formulation considered in this contribution does not tackle RVE mesh-dependency, which persists due to microscopic softening sources. The impact of micro softening is examined by adopting a nonlocal version of the damage model, yielding an important reduction in RVE mesh-dependency. Attenuating micro mesh-dependency increases the effectiveness of macro-scale regularisation. These findings demonstrate the intricate interplay between mesh-dependent effects at both scales, particularly in the presence of strong localisation.