Just capture value of the RecordID that you just modified in the calling code, and pass it into the code to be dynamically executed:

@query = 'DECLARE @RecordID AS Varchar(12)

SET @RecordID = ''' + CAST(@RecordID_Updated AS varchar(10)) + '''

SELECT t1.column1, t2.column1, t2.column2

FROM Table AS t1

INNER JOIN Table2 t2 on t1.RecordID = t2.T1RecordID

WHERE t1.Record_ID = @RecordID'