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;

Look for function (ITVF) dbo.DelimitedSplit8K,