How to keep a live backup of an SQL server in sync?
Have you looked at SQL Server mirroring? You can have high safety mirroring which means that a transaction at the client is not done until the transaction has been mirrored to your data center database. Mirroring is done at the database level and there are different types of mirroring depending on your needs.

Please look at the following to see a more extensive description of mirroring:
https://msdn.microsoft.com/en-us/library/ms189852.aspx