In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we deal with the vector-valued intrinsic square functions, which were introduced recently by Wilson. In his fundamental work, Wilson established strong-type and weak-type estimates for vector-valued intrinsic square functions on weighted Lebesgue spaces. The goal of this paper is to extend his results to these weighted amalgam spaces. Moreover, we define vector-valued analogues of commutators with \(\mathrm {BMO}({\mathbb {R}}^n)\) functions, and obtain the mapping properties of vector-valued commutators on the weighted amalgam spaces as well. In the endpoint case, we also establish the weighted weak \(L\log L\)-type estimates for vector-valued commutators in the setting of weighted Lebesgue spaces.