Make sure you're also looking at the schema name along with the table name.  Maybe the schema is not "dbo" and so it looks like the table's not there when...

As noted, a name, "sd", that follows immediately after a table name, "sys.databases", becomes an alias for that table.  In fact, it becomes the only name for that...

I suggest generating a pattern to identity what the phone string contains.  Then all you need to do is decide which patterns are acceptable and which aren't.

For example,...

For only 1 to 5 rows, then it should'n take long at all. 

I don't see why SERIALIZABLE would be needed at all for this UPDATE.  SQL will...

Yes, SERIALIZABLE is the most restrictive level there is, so it could lead to blocking.

Is the main table indexed in some way on col3?

SET ANSI_NULLS ON
SET QUOTED_IDENTIFIER ON
GO
CREATE TRIGGER [dbo].[TriggerUpdateInsert]
ON [dbo].[TABLE_SOURCE]
AFTER INSERT, UPDATE
AS
SET NOCOUNT ON;

UPDATE TD
SET FIELD_1...

I think a well-written function might still be the best choice.  The logic could get very complex to implement trying to use a table structure.  If necessary for performance, make...

I'd use a cross tab within the CROSS APPLY to reduce overhead (I would think).

IF OBJECT_ID('tempdb.dbo.#your_table') IS NOT NULL
    DROP TABLE #your_table;