Why dont you do yourself a favor and DateTime.Parse your strings and use Date comparison operators
Something like
Function ObjectInRange(ByRef obj As Object, ByVal str1 As String, ByVal str2 As String) As Boolean
Dim date1 As DateTime = DateTime.Parse(str1)
Dim date2 As DateTime = DateTime.Parse(str2)
Dim inRange = False
For Each prop As PropertyInfo In obj.GetType().GetProperties()
Dim propVal = prop.GetValue(obj, Nothing)
If propVal Is Nothing Then
Continue For
End If
Dim propValString = Convert.ToString(propVal)
Dim propValDate = DateTime.Parse(propValString)
If propValDate.CompareTo(date1) > 0 And propValDate.CompareTo(date2) < 0 Then
inRange = True
Exit For
End If
Next
Return inRange
End Function