Not able to modify tables on remote SQL Server 2012 database

Question

I have Visual Studio 2010 installed on my Windows 10 PC. My website is on a shared hosting environment and utilizes a SQL Server 2012 database.

The hosting provider doesn't have web interface to manage database so I connect from the Visual Studio 2010 itself for management purposes.

Right now I am able to connect to the database and run my website locally but when I attempt to open table definition, I get this error:

This server version is not supported. Only servers up to Microsoft SQL Server 2008 are supported

Before upgrading to Windows 10, I was able to edit/add tables from Visual Studio 2010 Server explorer but now limited to read purposes only. This Windows 10 and Visual Studio is completely fresh install with nothing kept or saved from earlier windows version. I don't remember if I installed any SQL Server 2012 tools in earlier windows for managing the database from Server Explorer in Visual Studio.

I have searched a lot and even tried installing SQL Server 2012 Express which failed. Now, I am downloading SQL Server 2012 Management Studio from the same link to see if that will work. It will download in an hour or so but I don't remember downloading it earlier so wanted to ask you what can be done.

All I want is the ability to add/modify tables of SQL Server 2012 database from Server Explorer in Visual Studio 2010. Please tell me how can that be done and which tools are required for this purpose.