Just a couple of thoughts to throw in to the mix before you press the Go button...
Streaming doesn't give you all the programs from the main channels. It's called Catch-up TV for that reason. It's a curated list of the most popular programs, but not a like-for-like of what's being broadcast right now and for the next hour or two. If your mother has a routine, say some program she watches regularly on a certain evening at a specific time, then Catch-up might not be the most appropriate solution for her.
Another thing is the layouts are different. Some people are okay with this. Others prefer it where they have the same program guide and way of working no matter which TV they're viewing from.
Finally, if history shows us anything it's that TV manufacturers tend to put the lowest spec hardware in to their sets. This means that as the Apps develop and new features are added, relatively new TVs of three or four years old can start to lose functionality. This is because the chassis they're based on is much older than the model number and release date of the TV. We saw that happen with lots of Samsung and LG TVs losing the BBC iPlayer App. It wasn't just them either; other manufacturers have been affected similarly too. What we haven't heard is loads of complaints about older Firesticks. The conclusion we can draw is that for £30 (SD/HD) and £50 (SD/HD/UHD) they're a safer bet. I know you're planning on buying a Firestick, so this is really about your TV choice: Focus on "is it a good TV, with decent sound, and easy to use" rather than how many Apps it supports today.
Thinking about usability, where someone is used to the way Sky works, and they'd like that sort of functionality but without any extra bills, then it's possible with a Sky or Sky HD to send the TV signal from that box to another TV elsewhere in the house. Further to that, with an inexpensive IR receiver and the SKy remote, all the features of the box from the lounge can be enjoyed elsewhere in the house. This means the same TV guide, and access to programs already recorded, and the rewind/pause live TV feature, and setting recordings in the Planner.
Some older SkyHD boxes have an aerial output (RF2) on the back of the box. The later generation boxes replaced it with a little multi-pin port in to which an RF adapter could be fitter. Adding a length of coax cable, and fitting a Sky 'magic eye' IR receiver is about all that's required for the hardware.
Where someone has changed over to Sky Q then this is no longer available. There are other solutions for that.
Where you plan to buy a Firestick anyway, get one and let your MiL play around with the Catch-up TV facilities on the main lounge TV to see how she gets on with it. If okay, move it to the bedroom once a TV is purchased, or simply add it to a dumb TV to make it smart.
However, if Catch-up doesn't cut it, and she's still dead-set against an aerial on the roof or in the loft, then, as long as she isn't a Sky Q customer, consider the option of sharing the main Sky box to the bedroom.
