After turning your sample into valid XML, I was able to query it with T-SQL

DECLARE @xml XML = '

<CompoundLogData>

<ArrayOfEntry>

<Entry>

<DataType>Session:City</DataType>

<Value type="xsd:string">Glen Allen</Value>

</Entry>

<Entry>

<DataType>Session:State</DataType>

<Value type="xsd:string">VA</Value>

</Entry>

<Entry>

<DataType>Session:ZipCode</DataType>

<Value type="xsd:string">74115</Value>

</Entry>

<Entry>

<DataType>Session:Childrens</DataType>

<Value type="q1:AddEditChildViewModel"/>

<Child>

<ChildFirstName>ABC</ChildFirstName>

<ChildLastName>TTT</ChildLastName>

<BirthMonth>5</BirthMonth>

<BirthYear>1999</BirthYear>

<MemberId>0004554</MemberId>

<IsRemoved>false</IsRemoved>

<HasFreeMembership>true</HasFreeMembership>

</Child>

</Entry>

</ArrayOfEntry>

</CompoundLogData>';

-- Look at the individual "Entry" nodes

SELECTc.query('.')

FROM @xml.nodes('CompoundLogData/ArrayOfEntry/Entry') T(c)

/* Retrieve all columns, based on assumptions about the sample XML

There will be one or more ArrayOfEntry nodes

Only the first Entry node for City, State, and ZipCode will be shown for each ArrayOfEntry

The cardinality of the "Session:Childrens" nodes is not specified, so this assumes it is 0, 1, or many

The Value/@type attributes are not used, assuming they are not necessary

*/

SELECTCity = ArrayOfEntry.value('(Entry[DataType = "Session:City"]/Value)[1]', 'varchar(50)'),

State = ArrayOfEntry.value('(Entry[DataType = "Session:State"]/Value)[1]', 'char(2)'),

ZipCode = ArrayOfEntry.value('(Entry[DataType = "Session:ZipCode"]/Value)[1]', 'varchar(15)'),

c.*

FROM @xml.nodes('CompoundLogData/ArrayOfEntry') T(ArrayOfEntry)

OUTER APPLY (

SELECTChildFirstName = Child.value('ChildFirstName[1]', 'varchar(50)'),

ChildLastName = Child.value('ChildLastName[1]', 'varchar(50)'),

BirthMonth = Child.value('BirthMonth[1]', 'tinyint'),

BirthYear = Child.value('BirthYear[1]', 'smallint'),

MemberId = Child.value('MemberId[1]', 'varchar(50)'),

IsRemoved = Child.value('IsRemoved[1]', 'bit'),

HasFreeMembership = Child.value('HasFreeMembership[1]', 'bit')

FROMArrayOfEntry.nodes('(Entry[DataType = "Session:Childrens"]/Child)') p2(Child)

) c