What are the key-features that enable an information diffusion model to explain the inherent dynamic, and often competitive, nature of real-world propagation phenomena? In this paper we aim to answer this question by proposing a novel class of diffusion models, inspired by the classic Linear Threshold model, and built around the following aspects: trust/distrust in the user relationships, which is leveraged to model different effects of social influence on the decisions taken by an individual; changes in adopting one or alternative information items; hesitation towards adopting an information item over time; latency in the propagation; time horizon for the unfolding of the diffusion process; and multiple cascades of information that might occur competitively. To the best of our knowledge, the above aspects have never been unified into the same LT-based diffusion model. We also define different strategies for the selection of the initial influencers to simulate non-competitive and competitive diffusion scenarios, particularly related to the problem of limitation of misinformation spread. Results on publicly available networks have shown the meaningfulness and uniqueness of our models.