Not to be grammatically picky, but if you are going to send that letter you need to take the apostrophe "s" off of PNM. If you are talking about PNM in the plural sense there is not apostrophe as they are not possessing something, for example.
Ex.1: The PNMs this year are so great! They are all very outgoing and have a lot of spirit. (There is no apostrophe here because you are talking about them as a group.)
Ex. 2: The PNM's dress was so beautiful so I asked her where she bought it. (Here you would use the apostrophe "s" because the PNM is possessing something.)
When something is made plural in the English language it is usually done by adding an "s" to the word, not apostrophe "s". It is a very common mistake, but one that drives me crazy.
Can you tell that I am a teacher?
In another respect, I don't necessarily know that sending it to the chapter adviser is a good idea, as she might be "close" with the girls and just think you are being a bit overbearing and unkind. We all want to think the best of the chapters we advise, and when something like that comes, regardless of whether or not it is true we don't want to start an all out war because their adviser may not be mature enough to look at it in a way that is conducive to fixing the problem. You said in the letter that you are not an adviser and you are a concerned alum. While I see your point, I don't think that you are going to come off in that way.
Sorry for being harsh, (was I?) but you asked, and really this could open a can of worms that just doesn't need to be opened. Why not just rise above the other chapter by being more panhellenic on campus, doing some great PR for AGD, and proving them wrong to begin with? If the other chapter is telling stuff to the PNMs that is unflattering, and they(the PNMs) see that it isn't true, then who looks bad? Certainly not AGD.
*edited because I kept adding on when I thought of new stuff.*