I am not sure I got 100% what your need is. Am I right in saying that what you want to do is:

1. Selecting a set of nodes starting from the "producer" or the "problem"
2. Getting your menus organised by "problem" (if you selected them by "producer" or by "producer" (if you selected by "problem")

???

The easiest way that comes to my mind is to use taxonomy_block or taxonomy_menu (the latter will fail to honour your URL alias, though) to generate a menu based on either "producer" or "problem", and a views filter (of which you can tweak the UI if you like) that when clicked will display only the subset of nodes meeting your needs.

Of course there are another gazillion ways to get the same result, from re-generating the menu dinamically to create a "pivot table" merging both taxonomies and using the terms as tags.