Beware circular references. They are very easy to create if you start passing references to the current object you are in, into other sub-objects, which may hang onto them.
Your current plan also sounds more like the objects are inter-dependant, rather than one inheriting from the other.

Widget and Widget::Checkbox are not separate objects, merely one object spread over 2 packages. I would suggest separating them, keep Widget as a base class, which knows nothing about Widget::Checkbox. Let Widget::Checkbox (and Widget::Radio and Widget::Foo extend Widget)

In one of my current projects, I use a base object, which contains these methods:

# initialize/bless/ect
$obj->new();

# serialize the objects data (currently with Storable)
$obj->serialize();

# get/set params as in CGI.pm
$obj->param();

# deserialize the objects data (Storable)
$obj->deserialize();

# xml format
$obj->to_xml();

# de-xml
$obj->from_xml();
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All of my other data objects, inherit from this object. A few, override the object's methods such as param, if I need a specific behaviour. (such as throwing an exception if I get bad data passed in)