Can I throw my sixpennyworth in?
I no longer work in an office, or for anyone else - hurrah! - but I do remember how awful office politics can be.
In my last company I had an executive role, and we had secretaries who supported 3 or 4 people, so I had to manage my own quarter of a secretary. I had the additional responsibility of managing all the secretarial and support staff in the company. I've also been a secretary, so perhaps can see things from both sides.
Based on bitter personal experience, the first thing I would say, which might sound horribly politically incorrect, is to ask you "what would a man do"?
The reason for that is that men - IME and IMO - are much, much less likely to get involved in the emotions of any office relationship, and they are often much more able to set clear boundaries between work and leisure.
Stop worrying about being nice or pleasant to this woman, as she is obviously only using this against you.
Stop confiding in your colleague. He will not help you - indeed he may well make things worse for you.
Be professional, be calm, be clear and above all be fair and consistent.
Make sure that you know what her role/responsiblities are. It may seem trivial, but if it's not her job to type a letter like this, then you are being unfair. (I can't think that this would be the case, but make sure you do know what you can/can't ask her to do for you).
Then do your job and manage her so that she does what you need from her.
If she kicks off, deal with it calmly and make it very clear by the way that you respond that it is she who is being ridiculous. Shouting at you in the middle of the office is childish and immature. But how did you handle it? Did you get drawn in? Did you respond? Or did you say something like "when you have finished, perhaps you would like to come into my office and tell me what is wrong?" i.e. being cool and superior, without getting involved.
You don't have to be liked to get on in an organisation - but somehow we always want to be liked. It is a very human need.
But we do need to be respected. Which is why knowing what her role allows/does not cover is vital - along with appropriate communication.
Don't go to HR with this as this will give them evidence that it is you who can't behave as a manager.
Sorry if this sounds harsh, but I think you have allowed emotions and feelings to cloud what should be a very simple part of the office dynamic.