If someone is truly mentally ill there are very few things you can do to "deal" with them b/c their actions aren't based on rational thoughts and reasoning.
I would suggesting ignoring the behaviors unless your children are involved. If she yells at your children (or anyone else's) again, don't yell at her b/c you will feed into "the crazy", but say firmly- "It is not your responsibility to discipline my child. If you feel he has done something, come to me and I will deal with it." Ignore, ignore, ignore and don't confront. It will only make the whole situation worse.
As for the husband, if he's neglecting his property, call the town and file a complaint but you can't change who he is.
We live in a very tight neighborhood as well, so I know how readily "one bad apple" can really spoil the whole bunch! The woman who lives two streets over from us is a genuine "hoarder" and it is both disgusting and sad, but not much we can do about it (aside from having people take the "long way" to our house).
Good luck and remember that in many cases, great fences make great neighbors- think about it!