When going manually, this works:

    ' Clone this object
    Public Function CloneManually() As Data
        Dim loData As Data = Nothing
        Dim loDataSet As DataSet = Nothing

        ' Get the proper definition as per the current scope
        If oProcess Is Nothing Then
            loData = New Data(oApp)
        Else
            loData = New Data(oProcess)
        End If

        loData.oDataSet = oDataSet.Copy
        loData.nCount = loData.oDataSet.Tables("Temp").Rows.Count
        loData.oDataView = New DataView

        ' If we have no record
        If nCount = 0 Then
            loData.oRows = Nothing
        Else
            loData.oDataView = loData.oDataSet.Tables("Temp").DefaultView
            loData.oRows = loData.oDataSet.Tables("Temp").Rows()
        End If

        Return loData
    End Function

There seems to be something when going through the MemberwiseClone() that puts something in memory which would make it not workable in my case.

When you mentioned the copy approach, is this pretty much what you had in mind?