Show terms in view filtered from another view
You don't need two Views Display for that, you can do that one with one Page Display. 


Create Views of type Taxonomy term and add Page Display 
Add Filter for Food Vocabulary 
Add the Parent Relationship. It is called Taxonomy term but look at the Description The parent term of the term. This can produce .... 

If you Require it the results will only show terms that have Parent items, so you'll probably want that. 
Add Contextual filter Name from the Taxonomy term Category and configure it:
Relationship: Parent
When the filter value is NOT available
Display a summary
Format List
Base path (you must enter the Page path if this isn't the first Page Display in your Views)
Display record count with link
When the filter value IS available or a default is provided
Specify validation criteria
Taxonomy term name
[Food]
Transform dashes in URL to spaces in term name filter values
More
Transform spaces to dashes in URL


You will see a list of your parent items in the results (as a Summary), then when you click on one you will see Views results terms that are its children.