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sql - How to extract values from column and update result in another column

i have this table:

CREATE TABLE MyTable (
    IdDate int,
    FullDate varchar(255)
);

insert into MyTable (IdDate,FullDate)
VALUES (0, 'No1 (26) - Friday 4, January 2014'),
       (0,'No2 (64) - Monday 10, February 2015')

I wanna extract from FullDate something like this:

1 2014 01 04
2 2015 02 10

1st number is extracted from No1
2nd number is extracted from Year
3rd number is extracted from Month (convert January to 01)
4th number is extracted from day (if day < 10, add 0 at the beginning: 01,02... )

And update the new value extracted in first column called IdDate

My final result should be like:

IdDate        FullDate
120140104     No1 (26) - Friday 4, January 2014
220150210     No2 (64) - Monday 10, February 2015
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If open to a helper Table-Valued Function:

Example

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

Returns

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

If it Helps with the Visualization, the TVF Returns

enter image description here

The Function if Interested

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 
)

Or Without the Function

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

EDIT

This is an expanded version of Shawn's cleaner solution

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

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