How to change toggle for some words in a string

In short NO there is not a simple instruction.

You could utilise some useful SQLite inbuilt functions (as per https://www.sqlite.org/lang_corefunc.html), notably substr, upper and lower.

Consider the following demo (which assumes that the table is named x and there are two columns, one for the relationship and another for the occupation)

The demo includes 3 queries, the first just extracting the corrected data, the second introducing how that can be used to drive a CTE (temporary table) and the third showing how the CTE can be used to drive an UPDATE of the actual table (table x):-

DROP TABLE IF EXISTS x;
CREATE TABLE IF NOT EXISTS x (id INTEGER PRIMARY KEY, relationship TEXT, occupation TEXT);

/* Add some data */
INSERT INTO x (relationship,occupation) VALUES
    ('Relationship: Wife','Occupation: Unpaid domestic duties'),
    ('Relationship: Wife','Occupation: Unpaid domestic Duties'),
    ('Relationship: Wife','Occupation: Unpaid Domestic Duties'),
    ('Relationship: whatever','Occupation: whatever'),
    ('Relationship: brother in law','Occupation: Unpaid Domestic Duties'),
    ('Relationship: BROTHER IN LAW','Occupation: Unpaid Domestic Duties'),
    ('','') /* To show result of empty*/,
    (null,null) /* To show result of nulls*/
;

/* OUTPUT 1 */
/* Query to just extract the data */
SELECT 
    *, /* ALL rows*/
    /* PLUS a new column for the modified/corrected relationship column */
    'Relationship: '
        || upper(substr(relationship,1 + length('Relationship: '),1))
        || lower(substr(relationship,2 + length('Relationship: '))) 
    AS newR,
    /* PLUS a new column for the modified/corrected occupation column */
    'Occupation: '
        || upper(substr(occupation,1 + length('Occupation: '),1))
        || lower(substr(occupation,2 + length('Occupation: ')))
    AS  newO
FROM x;

/* OUTPUT 2 */
/* As above but as a CTE (Common Table Expression aka a temporary table) */
WITH
 cte AS (
    SELECT 
        *,
        'Relationship: '
            || upper(substr(relationship,1 + length('Relationship: '),1))
            || lower(substr(relationship,2 + length('Relationship: '))) 
        AS newR,
        'Occupation: '
            || upper(substr(occupation,1 + length('Occupation: '),1))
            || lower(substr(occupation,2 + length('Occupation: ')))
        AS  newO
    FROM x
 )
SELECT * FROM cte
;
 
 /* As above but as a CTE (Common Table Expression aka a temporary table) */
WITH
 cte AS (
        SELECT 
        *,
        'Relationship: '
            || upper(substr(relationship,1 + length('Relationship: '),1))
            || lower(substr(relationship,2 + length('Relationship: '))) 
        AS newR,
        'Occupation: '
            || upper(substr(occupation,1 + length('Occupation: '),1))
            || lower(substr(occupation,2 + length('Occupation: ')))
        AS  newO
    FROM x
 )
UPDATE x SET relationship = (SELECT newR FROM cte WHERE x.id=cte.id), occupation = (SELECT newO FROM cte WHERE x.id=cte.id)
 ;
 /** 3rd OUTPUT i.e. the updated/corrected table */
SELECT * FROM x;

/* Cleanup the demo environment */
DROP TABLE IF EXISTS x;

• if the relationship and occupation are in a single column they the above could be used for the basis but would need modifying to suit.

The 3 outputs are as follows:-