Chris

If remote line tests are clear, then the problem is likely to be with the wiring or equipment in the house. This isn't guaranteed - there can still be faults that the remote test cannot detect, but it's less likely.

You need to get another corded phone and lend it to her for a couple of weeks. Open up her BT Master Socket and plug the phone directly into the test socket you'll find inside it. That way you are removing all of her own equipment and any internal extension wiring from the equation. If she can use the phone for a while without the problem recurring, you've isolated it as far as being either her own cordless phone, her own corded phone, or internal wiring.

From here you need to test her own kit a piece at a time. First plug her corded phone into the master test socket for a week. Then the cordless (but remind her to keep the corded phone next to the socket in case of emergencies), then close up the master and reconnect everything as normal. It's fairly likely that at some point in that process, the problem will reappear and you'll have found the culprit. If you go through all this and find no fault at all, then you should be able to call TalkTalk and insist they escalate it to BT to send an engineer, and be pretty confident that BT will find a problem somewhere that doesn't result in your mum-in-law being charged.

If at the end of this process BT somehow find a fault in her set-up that you have missed, and she gets charged for the callout, that's unfortunate but in the long-run I'd say it's better to have the problem isolated and professionally repaired than to let it potentially get worse and have her cut off entirely ...