When writing a letter applying for any type of position you should keep it short, sharp and concise. Make sure you address the right person and begin the letter with all of your personal information including your full name, address, phone number, email address and any other relevant details. You will then need to address the right person - head nurse/head of department - and explain the situation and how much you'd like to do the job again. Explain the situation you are in and how the position directly relates to your previous roles. You must make it clear how enthusiastic and keen you are to progress despite your initial failings. Try to explain what you have done or are doing to correct your previous failed efforts and what you have learnt that has helped to get yourself back on track. Include any information that backs up your claims and then get some recommendations from previous employers or testimonials in the form of a letter and enclose them accordingly. Talk to people who have achieved their status in nursing and find out the problems or issues you might face. They may be able to intervene on your behalf with the appeals committee. Submit your request to the specific department and be patient as appeals can usually take a few weeks to process.
Very politely, showing what you have done to improve the position you are seeking. In polite and truthful terms explain why you are the person they are looking for. There is some reason you have failed twice and address what you have and are doing to change the failure into a success. Show anything inside and outside their definitions that will get their attention. Accept responsibility for your actions and explain and stand by your promises for future behavior. We learn from our failures.