Hi Florent,
We will use Advanced Find to search out such views.
I simulated your environment.
Household 1 has two related contacts. They each have two related cases.
Here the lookup field for the relationship between Household and Contact is "Household", which will be used in advanced find.


For Household 1, I should be able to search out these 4 cases.
Open the Advanced Find, Look for Cases. First select (Related) Contact, then select the (lookup field) Household, then select the Household record you want to view.

Click Result button, you will see all related cases.

Save this view. Note that this view is a view of case, not a view of Household.

The next time you want to see related cases of another Household, you just need to modify the Household record after "Equals" in the filter.
After opening the saved view, open Advanced Find, change the Household record directly, and then save this view. Return to the view and refresh to see the new Household related cases.
