I created an assembly that was made flexible in another assembly. After putting the constraints of this assembly with the fixed, I would like to get it back in this position and make it rigid. The original assembly that was made flexible became totally "uncontrollable".
What you can do is create a configuration by use case of your subset.
Then open one of the head assemblies (the one where it's going well at the moment...), Take the configuration of your subset that will correspond to this use case and edit the subset in context (I say edit in context and not open)
Fix your components (all or part) in this configuration.
You can exit the in-context editing and make it rigid again. Now your subset should maintain its position in this configuration.