All the below statements will work on a MDB databank (No removing of quotes needed):
1). An Update query updating TWO fields, one with SINGLE quotes and one with DOUBLE quotes
UPDATE Personal SET Personal.LastName = "Test'Single", _
Personal.FirstName = 'Test" Double'
WHERE Personal.PersonalNr="0010101";
2). A Select query with criteria on a field that contains a SINGLE quote
SELECT Personal.PersonalNr, _
Personal.LastName, _
Personal.FirstName
FROM Personal
WHERE Personal.LastName="Test'Single";
3). A Select query with criteria on a field that contains a DOUBLE quote
SELECT Personal.PersonalNr, _
Personal.LastName, _
Personal.FirstName
FROM Personal
WHERE Personal.FirstName='Test" Double';
It only matters on how you build the SQL statement, in which a function would make it easy to check for the presence double or single quotes, (Using InStr), and add the needed surrounding quotes.