Ideally - the parameter is connected to a (or the same) parameter in the host when the family is built. That way you only need to manipulate the host family and all changes cascade down into the nested families.
If the nested family is shared - you can access its type properties directly either through the browser or by tabbing into the nested component and doing edit type. If you want the instance properties - you can just tab to the element ad adjust the properties directly. No dynamo needed - but these will be visible to Dynamo as normal family instances.
If the elements are not shared - it is “locked’” in as a dumb element. Rhythm has a node to get the nested elements - but only if they are shared.
Bottom line - this is more of an issue of content creation. Link your parameters.