We swapped router boxes and now life's complicated - help!

[#1]

Can anyone help me with a (slightly bizarre) problem? I'm scandalously untechy, and my other half only understands TV technology, so we're a fairly hopeless pair.
My elderly mother lives in an annexe to our house and we have separate telephone lines and separate router boxes. We did consider sharing a wireless internet connection at one stage, to save on costs, but the house is too elongated and the walls too thick for one router box to do the trick and I wasn't confident about getting boosters to work successfully. The telephone points in our (older) side of the house are in very strange places, with old and unreliable cabling between them, and I'm not sure we've ever got to the bottom of which one is the principal socket.
Both Internet connections worked tolerably well for a while - there's no cable Internet out here in the sticks and broadband's never been particularly speedy - until ours dropped out entirely a couple of years ago. Blaming the elderly router, we bought a new one and set it up as per instructions. But it didn't work. We then found out that Plusnet (our mutual ISP) could send us a new one for free. We set this one up, but still it didn't work. In desperation, we gave my mother the new Plusnet router (which worked) and plugged her old one into our line. Bingo!
A few months later, my mother mentioined that she was getting emails advising her that she was approaching her monthly usage limit. She had a very basic package, but was rarely online, so it didn't make sense. On investigation, it transpired that, by swapping router boxes, I had starting using her Internet package (but on our phone line, which wasn't the one registered to her account) and vice versa. I've never quite been able to get my head around this, but didn't want to mess up our connections again by rejigging things. So I increased the limit on her account (the one I was now using) and decreased it on mine (now hers) and paid the extra.
Fast forward to this week. Our router box now has no Internet connection and nothing I can do to it by way of resets is making any difference. Given that it's a fairly elderly box, with a tendency to overheat (I use a timer to switch it off overnight), an obvious thing to do would be to buy a new one. But I'm terrified of setting a new one up - whose settings do I use? those from my Plusnet account or hers? - and of somehow messing up her connection.
Help, please!

[#2]

Hello there,
Not to worry if you're not too knowledgeable about this sort of thing. You've described the issue quite well and I can suggest a few ways around this.
Just to mention, although I've not been able to look at your account in particular yet it's very likely that the reduction in speeds for your connection has been caused by the router being powered off every night. To cut a long story short the way in which the type of connection I believe you have works means that if a high number of disconnections or long periods of disconnections are detected by exchange equipment the speeds are lowered as a precaution, so we would advise to avoid doing that if at all possible.
It's also probably best that we get the account details for the 2 connections swapped back over, we do have a way of doing this remotely so we won't need to talk you through doing anything long-winded or complicated. And with regards to a new router for yourself we can offer you one that would be free (unless you decided to cancel within 12 months plus £4.99 postage and packing to place the order) I can use the same method that I've just mentioned to make sure that all you have to do is plug the router in and leave it to it and within 15 minutes it should configure for your account details automatically.
I'm aware that you'll probably need to change the limits on each account so it might be easier if we have a chat over the phone and I can arrange all this for you. Feel free to send me a personal message on here (see the envelope icon under my forum username to the left of this reply) with your phone number and I'll be happy to call and sort this all out.
Adam