OP, on a personal and informal level, I think you're going through a very difficult time. I see that you've not made many personal touches to your property and I can see that as a sign of it.
I really don't agree with those saying that your house is too highly priced. Hartlepool is becoming quite gentrified and the proximity to the beach, coupled with the fact that it's a decent size and no apparent issues, such as mould or subsidence. I acknowledge that moving so soon after purchasing may be seen as a red flag but perhaps this could be mitigated with a notice on the listing that you are only moving due to personal circumstances.
Also, it can take several months to sell a property. Your listing has only been on since April. I wouldn't worry too much.
But do you think that it's the right thing to do to move? I appreciate that your mother is ill but surely moving places again would only cause her more distress? The house that your mother lived in before will have surely been sold now, so it won't be the same and they do say that home is where the family are.
Could you make a stable, familiar home for your mother at your current address? Your children (who the move would also unsettle) and you could provide her with re-assurance and familiar face and create happy moments there.
The more I think about this thread, the more I wonder if the sale of the property is an issue or if it's actually the OP not being sure of what they want to do.
OP, please read the Alzheimer's Society website for advice and support, for you, your family and your mother. There are ways to help people live with Alzheimer's and live good and long lives. Medication helps. Music helps. Playing your mother's favourite songs will bring her joy and also help her to stay clung to who she is and those around her.
I can't believe I didn't see this before, but given the thread title, I looked at it with my business brain.