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Split tunnel (allowing direct access to Internet versus routing all traffic through the VPN headend) is the default.
You change this in Global Properties > Remote Access > Endpoint Connect > Route All Traffic to Gateway
There is also a setting on the client when the above setting is set to "Configured on Endpoint Client." 

For access by DNS name, that generally involves:

• Configuring Office Mode (requires appropriate licenses). This will assign the VPN client an IP address on the configured network and, more importantly, DNS servers for the client to use.
• If you are using SecuRemote (which does not have license requirements), refer to this for configuring SecuRemote DNS objects: https://community.checkpoint.com/t5/Remote-Access-VPN/Quick-Primer-on-How-to-Configure-your-Gateway-...

Depending on the precise requirements for accessing the Disaster site, you may want to configure Multiple Entry Point.
See: https://sc1.checkpoint.com/documents/R81.20/WebAdminGuides/EN/CP_R81.20_RemoteAccessVPN_AdminGuide/C...