With the advancement of computational network science, its research scope has significantly expanded beyond static graphs to encompass more complex structures. The introduction of streaming, temporal, multilayer, and hypernetwork approaches has brought new possibilities and imposed additional requirements. For instance, by utilising these advancements, one can model structures such as social networks in a much more refined manner, which is particularly relevant in simulations of the spreading processes. Unfortunately, the pace of advancement is often too rapid for existing computational packages to keep up with the functionality updates. This results in a significant proliferation of tools used by researchers and, consequently, a lack of a universally accepted technological stack that would standardise experimental methods (as seen, e.g., in machine learning). This article addresses that issue by presenting an extended version of the Network Diffusion library. First, a survey of the existing approaches and toolkits for simulating spreading phenomena is shown, and then, an overview of the framework functionalities. Finally, we report four case studies conducted with the package to demonstrate its usefulness: the impact of sanitary measures on the spread of COVID-19, the comparison of information diffusion on two temporal network models, and the effectiveness of seed selection methods in the task of influence maximisation in multilayer networks. We conclude the paper with a critical assessment of the library and the outline of still awaiting challenges to standardise research environments in computational network science.