Many thanks for your patience. If there is a written contract in place and it contains a specific clause detailing the notice period an employee is supposed to give if they wanted to leave their employment, they will be contractually bound by it. Therefore, if the employee fails to honour this notice period then they will be acting in breach of contract. The employer then has the option of suing the employee to seek compensation for damages resulting from their breach.
So you cannot just penalise the employee for not working their notice period, meaning that any compensation you wish to get from them must be justifiable as genuine losses incurred as a direct result of their breach. So the fact that others had to do extra shifts is not a loss because you would have had to pay her to do the same time so no extra losses have been incurred there. The only potential losses are the extra advertising you have had to do as a result and you must be able to justify that these are necessary and unavoidable costs which you would not have otherwise incurred as a result of her breach.
In terms of the professional aspect of her actions, such as not administering the necessary medication, that could be professional negligence. For this you would need to report her to the relevant regulatory body, such as the NMC and they can take their own separate action to deal with her if necessary.
This is your basic legal position. I have more detailed advice for you in terms of the steps you need to follow should you decide to pursue the matter for compensation further, which I wish to discuss so please take a second to leave a positive rating for the service so far (by selecting 3, 4 or 5 stars) and I can continue with that and answer any further questions you may have. Don’t worry, there is no extra cost and leaving a rating will not close the question and we can continue this discussion. Thank you