I'm not sure I really understand your question.
You have a custom post type. When you say it should "contain different sub-categories" do you mean that the post type should have a taxonomy (such as categories) assigned to it?
So your custom post type could be "flowers" and you have categories "red", "purple", "yellow" etc.
Or do you mean something different when you say the post type should contain different sub-categories?
The typical URL structure for CPT posts is site.com/cpt-slug/post-name/.
You would like a different structure, site.com/cpt-slug/category/post-name/
If you edit the CPT at Toolset > Custom Post Types, the Options allow for setting custom rewrite rules, but that doesn't accept placeholders in the same way that the Settings > Permalinks page does.
To create such a permalink structure for your CPT you would need to either write custom rewrite rules in PHP, or use a plugin which provides a simpler way of creating custom rewrite rules that are more flexible than those offered by WordPress itself.
The structure you are proposing does seem inherently problematic, though, if your posts can have more than one category assigned (as only one category can appear in the URL).
Lastly, there is the question of using Divi or Toolset to design these pages. You talk about them as archives, but these are not archives, these are single posts we are describing, if I have understood you correctly.
In any case, you can choose to design templates for single posts with either Toolset or Divi, and likewise you can design custom archives with either Toolset or Divi. I can't really help with designing them with Divi, but if you need help designing them with Toolset we can help with that.
