You probably know from experience that parents can get angry quite quickly over issues that involve their children. If you are dealing with an angry mother, she might address you by yelling or she might take the time to send you a heated letter. Whatever the case, you could choose to respond with a carefully worded letter. This lets you put all of your thoughts in one place and will give her time to think about what you are saying, instead of reacting from the gut before you finish your sentence.
Allow the situation to breathe before you sit down to write the letter. This gives everyone a chance to cool down from the heat of the situation. It's easy to churn out a heated letter that is defensive and not well thought out, but this probably won't get you anywhere. Instead, give the situation a day or two so you don't feel so steamed up, and the upset mother will hopefully take the time to chill as well.
Write down exactly what you want to say. Think about the mother's feelings as well as your own. Try to understand both points of view. Initially, you will probably feel defensive. This is probably justified, but you are probably also trying to protect yourself and your family as well. It's okay to admit you could have done better -- if that was the case. Write down all the key points you want to address in point form so that you don't forget anything.
Write the Letter
Address the letter as appropriate to your relationship. This will probably be with a "Dear Susan" type of salutation. If you address the mother too formally it will sound terse, so keep it as friendly as possible. Break up each thought into a clear, concise paragraph. For example, "I'm sorry you feel I wasn't watching your child. I think this is a misunderstanding. While I was doing the dishes, my teenage daughter was keeping an eye on the kids. They were never left unsupervised." In the following paragraphs, feel free to explain any other issues or what you want from the relationship. "I really hope this doesn't harm our friendship. Our children get along well and I miss our chats. I'd like to continue having play dates and would love to watch Sally again if you are comfortable." Make sure you add an apology to the letter. It doesn't matter if you don't think you did anything wrong. You can apologize for the situation or the hurt feelings. "I'm sorry that this happened" or "I'm sorry your feelings were hurt" may be all is needed to smooth things over. End the letter with a salutation that expresses what you are feeling "Love, Lizzy" or "With the utmost sincerity, Lizzy."
Don't ship that letter off yet. Re-read it for grammatical errors and then let it breathe again overnight. This will give you the chance to add anything you might have forgotten or change anything that wasn't worded quite right. It's amazing how sleeping on something can change your perspective. Read the letter again the morning, and try to think about it from the mother's perspective. If you think you expressed yourself well and it will encourage the desired result, put it in the mail.