Detecting Conflicts
The easiest way to detect whether two prompts conflict with each other consists of knowing whether these should be visible right now.
If two prompts appear on the same type of object, the game cancels out both of them and none of them show up in-game.


Solving Conflicts
Now we come to the difficult part. Solving conflicts with different kinds of prompts vary on difficulty, based on how many prompts are appearing simultaneously and how many conditions are applied to their form.

To solve a conflict, go into xEdit or the Creation Kit and start searching for Perks that implement Activate entry points.
You can use Alternative Activation Prompts as an example.

There, you look under the Perk conditions. If the conditions of two different prompts are all true on the same object, they conflict, as said earlier, so you have to add a condition to cancel out the conflict, like checking whether the target has a certain keyword, or a different prompt is currently enabled and should be showing using a global variable.

That's basically everything anyone can do. The process is not simple nor easy, but it's somewhat manageable.