My mum is completely of the opinion that she's selling the house and not the furniture so I'll have my work cut out trying to make her see the importance of what you've all said
Whilst your mother is correct she needs to accept that she's now marketing one, if not the one, of her most important and valuable assets, so it makes sense to present it in the best light possible for current taste. The modernised kitchen and bathroom only serve to highlight how out of date the rest of the house is.
Unfortunately I'm not impressed by either of your agents, the photos and the blurb about a cherished family home, scope for further modernisation etc. just reinforces the message of some of the photographs that this home is in large parts a good 25 years behind the times. That's fine if it's how you want to live, but you're now reaching out to fresh eyes who are looking at how lovely the house is, or potentially is, but also, what they'd be required to spend on it over and above the purchase price and the work involved.
You've attracted lots of viewers, but in all honesty, you don't need loads of viewers, you just need one purchaser who can go ahead at an acceptable price. Unfortunately it looks like you missed the boat when next door was sold.
Personally I'd work on updating the living room, it's a very good opportunity to have a clear out and streamline things. Meanwhile I'd withdraw the house from the market. Two Agents puts me off, it smacks of 'this house won't shift'. In the New Year, towards Spring, I'd get some others around for honest appraisals and make it plain that when you go back up for sale the emphasis should be on the prestigious location.
I'd also get your Mother to work out what she actually wants, it's all a bit of an unnecessary strain if she isn't committed to selling anyway.