Firstly, yes, she is liable to pay the money back if it was paid in error. However, it is important that your mother firstly tries to obtain evidence that the money was paid in error and secondly, that the bank informed her about the issue properly.
A suitable next step would be to write the the bank, solicitors and debt collectors (I'd send them all the same letter) stating that your mother believes that she is entitled to the money which was left to her in her late mother's will. Your letter should include details of your problems in making contact and it should ask for full details of why the bank (NatWest or Halifax?) feel thet they are entitled to a repayment. The letter can also state that your mother was unaware of any problems and so spent most of the money on a holiday before being informed about any issues with the payment.
It is up to your mother, but she could also state that there is about £2000 left which could be paid in full and final settlement if it can indeed be established that the original payment was made in error.
Hopefully, you will at some point see the accounts of the executors of the will and hopefully this should clarify matters. Normally such accounts are shown to or made available to beneficiaries. It would not be sensible to accept that the payment was made in error simply because that is what the bank says.