I've done a ton of work on this over the years - including a lot of experimenting with remote cellular RS232 terminals (airlink raven, tellular, serial over IP + cradlepoint)... all I can say is that your success is really up in the air; some terminals are very strict in the data flow they expect and any delays/quirks really screw it up; some have good checksums and error handling and can survive just about anything - but its all in how the terminal was built.
I also do a lot of remote help with people and rather than opening up full remote access, what I do for the people I support is set up a computer in their house that has the necessary software and connectivity and either do remote support with them as needed, or even just set up teamviewer or logmein with unattended access - that way all the software needed is on premise and the connection is local; all I need to do is get to the remote PC.
The RS232 to IP converters work OK - especially for occasional use - you generally have to manually connect/reconnect when you go to use them but that's fine for what you're doing as long as they work otherwise - but as stated above, make sure that if you go opening up firewalls and all that, you're handling security appropriately. This is yet another reason I like the logmein solution - nothing is permanently bound to the existing network config or router - way too often end users will fall for the next big bundling service with uverse or verizon or comcast and have their modems/routers swapped out without any consideration for the manual port maps you've set up, then you get stuck troubleshooting it just to find out that they've undone all your work and now you need to go to their home to set things up again. logmein will be immune to most of that.