Just what is the best set up so she can use it. No internet, Youtube etc, just a means of streaming from my sat box to a tv.
Hey TJ, are we talking live streaming (of live TV channels), or a mediacenter of what's on the HDD or what?
And what degree of control do you need?
One possible solution is a n HDMI extender, coupled with an IR extender.
This let's your other half's TV display the output of the box, and the IR extender will let her control the box from afar.
This works for all boxes, as long as they have HDMI out and IR remote control (doing the most common NEC protocol, but's that probably too techincal).
User interface-wise, this means selecting an HDMI dedicated to the box, and then everything behaves as if the box was in the same room.
Second chouice is, if you just want to share the recorded content on the HDD of the STB, get an STB with a DLNA server built-in. There are several on the market. I am having plenty of fun with the Humax iCord Evolution.
It streams to my smart TV, and even transcodes and streams to my smartphone when connected over the same WiFi. Great for watching the latest news on the bog. (as iPlayer doesn't work here in DK).
This does not, however, do the freesat EPG, so planning your recordings is a bit more cumbersome...
Thirdly, If you are well-versed in PC-configuration and Linux, you can set up your own recording server, and share the content with many types of clients, including your smart TV. This can be MythTV base, or use somthing like TVHeadend - but they all have one point in common: They might install out-of-the-box, but to make them work the way YOU need 'em to work requires hand-on linux stuff, scripting, server configuration etc.
So - make up your mind of the "use case" for your redistribution of the SAT box, and you can choose what route to follow.