Potential Paths: Path 1: Use Twee due to its Story Generator feature which can enhance branching narratives, although it doesn't directly cater to adding images or any objects. Path 2: Use Pedagogical for its capability to support various content types, which potentially includes images. However, it does not directly support storytelling or branching narratives.

Final Narrative:

As per your request for a tool that supports storytelling with branching narratives, accompanied by relevant images and school-related objects, it seems that the available tools Pedagogical, Twee, and MagicSchool AI, do not fully meet your specifications.

However, Twee presents itself as a close match with its 'Dialogue and Story Generator' feature, which can be utilized to create engaging branching narratives. Although this tool does not explicitly mention a feature for adding images and objects, its functionality may still cater to your primary need for storytelling in pedagogical contexts.

Given the slightly fragmented alignment of your query with the available tools, I suggest giving Twee a try for the stories, and potentially complement its use with other digital tools meant specifically for incorporating images and objects.

Remember, it's always a good idea to test out different tools and assess their efficacy in promoting your students' learning experience. Exploring various products can help you find a unique combination that efficiently caters to your teaching needs.