Transfer row from 'parent' to 'child' without creating duplicate and without knowing all 'parent' columns
No one (or rather very few) uses "table inheritance", like that. That's a half-baked PostgreSQL feature which is used for some internal underpinnings exposed to the user in a fashion likely to confuse them. I'd highly suggest avoiding it. For more information see,


Using table inheritance instead of mapping tables


In your case though you can use a single-table hierarchy or self-referencing hierarchy,

CREATE SCHEMA master;
CREATE TABLE master.entities
(
  entity_id       int  GENERATED BY DEFAULT AS IDENTITY PRIMARY KEY,
  parent_id       int  REFERENCES master.entities,
  entity_name     text,
  entity_data      jsonb
);

INSERT INTO master.entities VALUES
  ( 1, null, 'Master', null),
  ( 2, 1   , 'Corp'  , '{"date_of_birth":"2018-07-05"}');



  I would like to be able to bring down a row that was added to the master.parties table and insert it into any of the parties tables in the other schemas (ie. corporate), without creating a duplicate row in the master table.


I'm not 100% sure what you mean here. Essentially the relations are not meta-data, it's data. So you have to have a duplicate row to have one entity under two parents. If you want to minimize duplication of the JSONB though you could outsource that to another table -- though I would probably not bother with it unless you have a desired answer as to how two parties will manage the data-stored in the jsonb.

Querying the above structure is slightly more complex, but you'll get the hang of it, you have to use a recursive CTE. You can find lots of examples of this under hierarchy,

WITH RECURSIVE t(id,parents,name, data) AS (
  SELECT entity_id, ARRAY[]::int[], entity_name, entity_data
  FROM master.entities
  WHERE parent_id IS NULL
  UNION ALL
    SELECT e.entity_id, parents||parent_id, e.entity_name, e.entity_data
    FROM t
    INNER JOIN master.entities AS e
      ON e.parent_id = t.id
)
TABLE t;

 id | parents |  name  |              data               
----+---------+--------+---------------------------------
  1 | {}      | Master | 
  2 | {1}     | Corp   | {"date_of_birth": "2018-07-05"}
(2 rows)


Note this schema also permits N-level relationships (you can create an almost infinite amount of children under children -- no additional tables required)