Rigol Ultrascope remote via Internet
I have had success using the Rigol TCP/IP.  There are three choices documented on page 14-3 of the Users Guide.  The one to avoid is "Auto IP".  This will give you and address on the 169.254 which is not routed.  I have used both DHCP and Manual, but I like Manual best, because the Rigol keeps its configuration.
If you use manual remember to set subnet mask and gateway so that packets will be routed.

Now the hard part begins.  You need to map a TCP port through your NAT router or firewall.  Found this in another post, "SCPI Sockets TCP 5025 Communication with the instrument Use this port to open a raw TCP/IP connection to send raw SCPI commands to the instrument".  Since you know how to use Wireshark, I suggest you get things working on a local connection first and sniff the port.

All of this is a lot of work.  You might consider a service that allows you to upload instrument data via HTTPS.  You run client software on your laptop or other computer that acts as a gateway between SCPI (communicates with oscilloscope) and HTTPS.

The services I know of are Initial State and GradientOne.  GradientOne has a "Live Remote Oscilloscope Waveform Capture" that let's you control an Oscilloscope remotely.  The scope happens to be a Rigol, but I think any oscilloscope that supports SCPI commands over VXI-11 would work.