Having multiple contexts for the same database can be useful if your database contains several database schemas and you want to treat each of them as a separate autonomous area. This is not clear from your code / requirement, if so.
If the tables you work with are in the same database and in the same schema, then I see no reason to use two DbContexts. Even if you have a validation error or an exception, you can still save logs in the same context in your table.
If you are trying to log errors and / or other relevant information, why not use log4net for logging?
EDIT
In my opinion, registration should be independent of your normal transactions, so you do not need to think about this scenario. At the same time, you can save and register in the transaction, but also register if there is an exception. If I'm missing something, I still don't see the need for two DBC texts.
See below for some transactional guidelines.
https://msdn.microsoft.com/en-us/data/dn456843.aspx
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