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If you modify the Start date for Team A Work, the bottom two tasks will simply slide to the right. In the screen capture below, please note how the slack has been displayed, and Team B's work has been modeled as a separate task that must complete at the same time as the Other Project Work task. This mean Team B's work would complete on Day 90. If there is truly a dependency that Team B cannot start until Team A finishes (Finish-to-Start dependency), and Team B needs five days, then the latest that you can start Team A's work is Day 76. If Team B's task is not modeled at all, then add it. If there are task dependencies that cannot be modeled with Project, then you haven't broken them down far enough.

Your final sentence tells me that you either need to decompose your tasks a bit more, or you are missing a task definition.

You can even display it on the Gantt chart, if that helps tell your story visually. Displaying the slack for the task (as suggested by Polymath) is a great method.

Dependency chart in ms project timeline