Here's an alternative:

declare @children int

set @children = 4

SELECT

string,

STUFF(string, start_of_integer_value, CHARINDEX('<', string, start_of_integer_value) - start_of_integer_value,

CAST(@children AS varchar(10)))

FROM (

SELECT '<key>Children</key><integer>2</integer>' AS string UNION ALL

SELECT '<key>Children</key><integer>123</integer>' UNION ALL

SELECT '<key>Children</key><integer></integer>'

) AS test_data

CROSS APPLY (

SELECT CHARINDEX('<integer>', string) + 9 AS start_of_integer_value

) AS assign_alias_name