Cómo extraer valores de la columna y actualizar el resultado en otra columna

Si está abierto a una función auxiliar con valores de tabla:

Ejemplo

Declare @YourTable table (IdDate int,FullDate varchar(max))
Insert Into @YourTable values
 (0,'Nº1 (26) - Friday 4, January 2014')
,(0,'Nº2 (64) - Monday 10, February 2015')

Update A
   set IdDate = substring(Pos1,3,10)
              + try_convert(varchar(10),try_convert(date,Pos6+' '+Pos5+' '+Pos7),112)
 From  @YourTable A
 Cross Apply [dbo].[tvf-Str-Parse-Row](FullDate,' ') B

Devoluciones

IDDate      FullDate
120140104   Nº1 (26) - Friday 4, January 2014
220150210   Nº2 (64) - Monday 10, February 2015

Si ayuda con la visualización, el TVF regresa

La función si está interesado

CREATE FUNCTION [dbo].[tvf-Str-Parse-Row] (@String varchar(max),@Delimiter varchar(10))
Returns Table 
As
Return (
    Select Pos1 = ltrim(rtrim(xDim.value('/x[1]','varchar(max)')))
          ,Pos2 = ltrim(rtrim(xDim.value('/x[2]','varchar(max)')))
          ,Pos3 = ltrim(rtrim(xDim.value('/x[3]','varchar(max)')))
          ,Pos4 = ltrim(rtrim(xDim.value('/x[4]','varchar(max)')))
          ,Pos5 = ltrim(rtrim(xDim.value('/x[5]','varchar(max)')))
          ,Pos6 = ltrim(rtrim(xDim.value('/x[6]','varchar(max)')))
          ,Pos7 = ltrim(rtrim(xDim.value('/x[7]','varchar(max)')))
          ,Pos8 = ltrim(rtrim(xDim.value('/x[8]','varchar(max)')))
          ,Pos9 = ltrim(rtrim(xDim.value('/x[9]','varchar(max)')))
    From  (Select Cast('<x>' + replace((Select replace(@String,@Delimiter,'§§Split§§') as [*] For XML Path('')),'§§Split§§','</x><x>')+'</x>' as xml) as xDim) as A 
)

O sin la función

Update A
   set IdDate = substring(Pos1,3,10)
              + try_convert(varchar(10),try_convert(date,Pos6+' '+Pos5+' '+Pos7),112)
 From  @YourTable A
 Cross Apply (
                Select Pos1 = ltrim(rtrim(xDim.value('/x[1]','varchar(max)')))
                      ,Pos2 = ltrim(rtrim(xDim.value('/x[2]','varchar(max)')))
                      ,Pos3 = ltrim(rtrim(xDim.value('/x[3]','varchar(max)')))
                      ,Pos4 = ltrim(rtrim(xDim.value('/x[4]','varchar(max)')))
                      ,Pos5 = ltrim(rtrim(xDim.value('/x[5]','varchar(max)')))
                      ,Pos6 = ltrim(rtrim(xDim.value('/x[6]','varchar(max)')))
                      ,Pos7 = ltrim(rtrim(xDim.value('/x[7]','varchar(max)')))
                From  (Select Cast('<x>' + replace((Select replace(FullDate,' ','§§Split§§') as [*] For XML Path('')),'§§Split§§','</x><x>')+'</x>' as xml) as xDim) as A 
             ) B

Esta es una versión ampliada del limpiador de Shawn solución

Update @YourTable 
   set IdDate = substring(left(FullDate,charindex(' ',FullDate)-1),3,25)
               +try_convert(varchar(10),try_convert(date,replace(substring(FullDate, charindex(',', FullDate) - 2, 100), ',', '')),112)


Select * from @YourTable