Remote database connection problem?
Yes, you can use SQL Server Management Studio, even if it's an Express version to connect to any SQL Server,you have TCP/IP connectivity to. Just launch it, enter the DNS host name or IP address in the 'Server Name' box and hit Connect.

Two things may prevent this from working:

Your SQL Server isn't set up for TCP/IP connectivity. This is the default setting from version 2005 onwards, and can be changed using the SQL Server Configuration Manager.

There is a firewall between you and your SQL Server blocking TCP/IP traffic. This is an entirely sensible construction: you do NOT want your database server to be available from the general Internet, as this is a huge security risk. In fact, if your hosting company allows this kind of access by default, I'd be looking for a different provider...

Anyway, what seems to be needed in your scenario is: a) the hosting company enabling TCP/IP on your SQL Server instance, b) them providing you with secure access to the IP address that instance is running on. This will involve some kind of VPN or SSH port-forwarding soluition, or at least an IP filter, where only 'trusted' IP addresses can access the SQL Server (which is not a great solution, but can be used if nothing else can be implemented). You'll have to discuss these requirements with your hosting company.