Is it possible to access children/parent widgets from a given widget, in a Flutter test?

Yes, you can use find.descendant and Element.ancestorWidgetOfExactType.

Examples:

// Finds a RichText widget that a descendant (child/grand-child/etc) of a
// tab widget with text "Tab 1"
find.descendant(of: find.text('Tab 1'), matching: find.byType(RichText));

// Finds a parent widget of type MyParentWidget.
tester.element(find.byType(MyChildWidget))
  .ancestorWidgetOfExactType(MyParentWidget);

ancestorWidgetOfExactType is deprecated, prefer using findAncestorWidgetOfExactType