Simple: you are doing it completely wrong. Never concatenate strings to build a SQL command. It leaves you wide open to accidental or deliberate SQL Injection attack which can destroy your entire database. Use Parametrized queries instead.
When you concatenate strings, you cause problems because SQL receives commands like:
SELECT * FROM MyTable WHERE StreetAddress = 'Baker's Wood'
The quote the user added terminates the string as far as SQL is concerned and you get problems. But it could be worse. If I come along and type this instead: "x';DROP TABLE MyTable;--" Then SQL receives a very different command:
SELECT * FROM MyTable WHERE StreetAddress = 'x';DROP TABLE MyTable;
Which SQL sees as three separate commands:
SELECT * FROM MyTable WHERE StreetAddress = 'x';
A perfectly valid SELECT
DROP TABLE MyTable;
A perfectly valid "delete the table" command
And everything else is a comment.
So it does: selects any matching rows, deletes the table from the DB, and ignores anything else.
So ALWAYS use parameterized queries! Or be prepared to restore your DB from backup frequently. You do take backups regularly, don't you?
That isn't the problem you have seen and this specific code isn't vulnerable, but it's symptomatic of the same cause and that means you urgently need to fix this through your whole app. When you do, the problem you have noticed will disappear as well because you are no longer passing a string based date to SQL, but the actual original DateTime value from the DateTimePicker, which means that SQL Server doesn't have to "guess" what date format you might have passed it. Pass the DateTimePicker.Value property directly as a parameter and there is no conversion needed, and no possibility of misinterpretation.
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