I believe you should use a microflow as source for the selectable objects in the reference selector for child object as the non-persistable page parameter rules out using Database or Xpath as source. Create an association between your parent and child (1 parent has multiple childs). Use this association to retrieve all child objects that belong to the parent object (return this list of childs if the parent is filled)
On the reference selector for the parent you should use an on-change microflow that refreshes the non-persistable object. This will re-obtain the list of child objects on your child object reference selector.