A bit of a hack, and if you're open to a helper Table-Valued Function.
Example
Declare @XML xml = '
<FormSearchFilter>
<OtherContent>Some Content</OtherContent>
<IDs>
<int>1</int>
<int>2</int>
</IDs>
<IDs>
<int>11</int>
<int>12</int>
<int>13</int>
</IDs>
<IDs>
<int>99</int>
</IDs>
<MoreContent>Some MORE Content</MoreContent>
</FormSearchFilter>
'
Select @XML = replace(cast(@XML as varchar(max)),RetVal,NewVal)
From (
Select *
,NewVal = stuff(replace(replace(RetVal,'<int>',','),'</int>',''),1,1,'')
From [dbo].[tvf-Str-Extract](cast(@XML as varchar(max)),'<IDs>','</IDs>')
) A
Select @XML
Returns
<FormSearchFilter>
<OtherContent>Some Content</OtherContent>
<IDs>1,2</IDs>
<IDs>11,12,13</IDs>
<IDs>99</IDs>
<MoreContent>Some MORE Content</MoreContent>
</FormSearchFilter>
The TVF was created because I tired of extracting content (left,right,charindex,patindex,reverse,...). It is a modifed parse/split function which accepts two non-like delimiters. Just to illustrate, if you were to run:
Select * From [dbo].[tvf-Str-Extract](cast(@XML as varchar(max)),'<IDs>','</IDs>')
The results would be
RetSeq RetPos RetVal
1 65 <int>1</int><int>2</int>
2 100 <int>11</int><int>12</int><int>13</int>
3 150 <int>99</int>
The TVF if Interested
CREATE FUNCTION [dbo].[tvf-Str-Extract] (@String varchar(max),@Delimiter1 varchar(100),@Delimiter2 varchar(100))
Returns Table
As
Return (
with cte1(N) As (Select 1 From (Values(1),(1),(1),(1),(1),(1),(1),(1),(1),(1)) N(N)),
cte2(N) As (Select Top (IsNull(DataLength(@String),0)) Row_Number() over (Order By (Select NULL)) From (Select N=1 From cte1 N1,cte1 N2,cte1 N3,cte1 N4,cte1 N5,cte1 N6) A ),
cte3(N) As (Select 1 Union All Select t.N+DataLength(@Delimiter1) From cte2 t Where Substring(@String,t.N,DataLength(@Delimiter1)) = @Delimiter1),
cte4(N,L) As (Select S.N,IsNull(NullIf(CharIndex(@Delimiter1,@String,s.N),0)-S.N,8000) From cte3 S)
Select RetSeq = Row_Number() over (Order By N)
,RetPos = N
,RetVal = left(RetVal,charindex(@Delimiter2,RetVal)-1)
From (
Select *,RetVal = Substring(@String, N, L)
From cte4
) A
Where charindex(@Delimiter2,RetVal)>1
)
/*
Max Length of String 1MM characters
Declare @String varchar(max) = 'Dear [[FirstName]] [[LastName]], ...'
Select * From [dbo].[tvf-Str-Extract] (@String,'[[',']]')
*/