I hope you are not planning on selling that Navajo rug!
The rug you have is large, and quite fine workmanship, from what I can see in the pictures. If you would like to learn more about Navajo weavings (including some places that may be able to value yours) please visit weavinginbeauty.com. I've found their website to be quite informative. They have quite good information on caring for Navajo weavings as well. I would encourage you to consider hanging it, instead of using it as a floor rug. The Weaving in Beauty website also has recommendations on proper hanging of Navajo weavings.
You stated it was a gift of appreciation to your folks. I would recommend that you find out all you can about the rug, the weaver, and the story (or stories) behind how it came into your folks' possession. Find out about the work they did at the Navajo Childrens Home, and listen to the stories of times back then. Find out who gave it to them, and in what circumstances. Find out who wove it, and find out all you can about the weaver and her family. What your folks did must have been quite appreciated. A rug that size, of that fineness of weave, took a long time to make. It is not a small token. True appreciation of the gift will come from understanding the background behind it.
The grey line you speak of is a spirit line, to allow the spirit in the pattern to be free, and not trapped. You won't find a spirit line in every Navajo weaving, but they are frequently found when a border would otherwise enclose a traditional design. Except for the red the colors look like Two Grey Hills (which usually does not use red). The various shades of brown grey, black, and white in Two Grey Hills do not come from dyes -- they are from combing together varying amounts of wool of natural colors (black, brown, and white). This takes a lot of work to get even colors, before the yarn is even spun. The yarn looks to be rather fine, and that, too, is a mark of quality in this rug. If your rug's non-red colors are natural and not dyed the value is that much higher.
BTW, there is no "back side" to most Navajo weavings. The manner of weaving creates the image on both sides.
One thing does bother me -- usually Navajo rugs have a small braid or tassle at each corner. These come from the manner in which the rug is finished and removed from the loom. Try to find out why there are no tassles or braids on the corners -- were they cut off? (I sincerely hope not.) If they were cut off this could cause structural decay in the rug.
I am no expert, but I do love Navajo rugs. I visit the Southwest each year, as I have family there. Some have worked in Navajo and Ute communities, and I ask more questions and listen to their stories every time I see them. I encourage you to look into the stories and the people involved in this rug. You will enjoy it all the more.
