In order for us to understand how things fit together, we need to see the whole span of your back yard. Stand at the center of back of house and take sequential, slightly overlapping pictures from complete left of complete right. (All pictures must be taken from same location.) Post the pictures and let's have a look.

Ok sorry about that. How about a panoramic?

If you can't zoom. Here is an imgur link. http://imgur.com/a/XmiUM

For most of the trees, it looks like their lower portions are never again going to have nice foliage. The unattractive/dying foliage could be cleaned off. There seems to be a need to screen above the fence and possibly even the fence. Screening material could come in the form of shrubs, small trees (for screening above the fence) or vines. (I don't know what grows there.) It could work like this IF the trees are first cleaned up. The foreground of the raised planter could be covered solid with low groundcover. Isn't there a low groundcover that you would be easier than the grass?

I doubt you will find that a gravel or rock mulch will be any better at weed suppression or maintenance than a more typical organic, bark or wood chip mulch. Weeds will still generate in the material that accumulates on the rocks and tend to be somewhat more difficult to remove in this material. And clean up or removal of leaf and other plant debris is a lot harder (not really necessary with an organic mulch - it all breaks down with time). And in a hot climate, like yours would appear to be, can create some issues with certain plants due to heat retention and reflection.