It has always been the case, and still is, that the best way to avail Wi-Fi coverage in all but the smallest use case is to deploy a "cellular" coverage pattern of multiple hot-spots using Wi-Fi Access Points all connected to some common cabled network infrastructure to provide (what I call) the "backhaul" link between the AP's themselves and between the AP's and the rest of the (cabled) network which of course includes connection to the Internet (however that may be achieved.)
Quite literally an "AP in each room" - the classic mistake is to deploy the "AP-s in the corridors" and wonder why it doesn't work very well when every single radio transmission has to pass through at least one wall - often more and AP's are "sparsely" deployed - ie lots of clients per AP. Deploy the AP's where the users are. When I did a couple of big deployments in educational establishment, (think lots of kids in classrooms with a phone in their pocket and an iPad on the desk) I put an AP in every classroom, more in the bigger classrooms, lecture theatres, cafeteria, and so on.
Obviously in a house an "AP in every room" is going to increase the cost, so one might choose some judicious deployment - say one in the main "living room," one in the master bedroom (and the kids will just have to lump it) or perhaps you want to give their bedrooms one each too, or perhaps one between them. Less important, one might assess, is the kitchen, bathroom, hall, porch, landing, stairs, etc. It's a bit of a value judgement depending on how much you want to spend.
The "trick" is how one establishes the backhaul links:
Best is over a cabled ethernet infrastructure of wires, switches, and (in very large and complex deployments) routers (I'm talking "proper" routers here, not SOHO get-you-on-the-Internet Omni-boxes,) though you are highly unlikely to need extra routers for SOHO.
If you cannot get the drills out and install the cabled infrastructure, then tunneled over the mains using powerline technology is probably next best.
It is also possible to use Wi-Fi technology for the backhauls, but that is compromised because any AP pairings that talk to each other for the backhaul transmissions will need to be close enough to avail good signalling conditions (both ways) and the "only-one-thing-at-a-time-can-transmit" nature of Wi-Fi often means that throughput ("speed" as users perceive it) can be compromised by Wi-Fi backhauls as the air
time has to be shared (as in competed for - it's anything but "fair) for both client-AP transmissions and backhaul transmissions. So called Wi-Fi "Repeaters" are a classic exemplar of this - that can clobber the throughout.
Some of there newer "whole home" and "mesh" systems and things like "tri-band" AP's/routers try to mitigate the throughput clobbering by using different radio channels for the client-AP and backhaul transmissions enabling both to occur concurrently. This certainly helps, especially in smaller deployments, but it's not the magic bullet that negates that wired backhauls is still a better option.
I believe (having not use any) some of the "whole home" type systems are beginning to bring to the SOHO realm things that have been long used in enterprise systems in that the AP's "talk" to each other to do things like distribute clients, handle the roaming hand offs more smoothly, establish the channel plan and so forth. Until fairly recently, this was exclusively the preserve of enterprise grade systems and SOHO AP's/Routers were all "stand alone" bits of kit that didn't talk to each other at all.
It's worth noting that such AP-AP cooperation features are not dependent on the type of backhaul you use. Forever, enterprise AP's that "talk" to each other have been capable of using Wi-Fi for the backhauls - sometimes called things like "mesh" links. So "managed" systems of collaborating AP's and "mesh" Wi-Fi links are not fundamentally inter-related or dependent on one or another, it just so happens that things marketed into the SOHO realm as "whole home" type systems often happen to do both. In an ideal world, "whole home" AP's would also be wired backhaul capable (as enterprise systems are) offering the best of both worlds, but it wouldn't surprise me to learn that many are not and there's some kind of "base" AP that (wired) connects to the "rest of the network" and all the others are Wi-Fi only.
For the best Wi-Fi experience, wait till she's at her mothers for a week end, get the drills out and install some UTP - you know you want to.
I've not used it, but others here speak well of Ubiquity as an easy to use/deploy managed Wi-Fi solution for small estates. You might care to see what others have to say about it.