Wow, I'm so sorry for your family's situation. I think you have been given some great advice.
The idea for her to take some time for herself once a week is great. I strongly advice a weekly baby-sitter for maybe 4-6 hrs a week. This will give your wife a chance to run errands "peacefully" and perhaps do something for herself as well with that time.
She is obviously overwhelmed. I think she might be able to relate to a lot of the young, overwhelmed mothers who have found order and stability in their lives with flylady.net. This website teaches how to bring back order and peace to the home so that one can again find "joy" - and it does it in a fun, silly way - even has stuff that makes the kids want to get involved and help. Oh, and all of her tips that mothers find sooo helpful, are free! I truly think this might help more than anything else, because until she feels like things are at least somewhat under control, she's going to continue to be stressed out, overwhelmed, depressed, etc. Of course, if she's truly "clinically" depressed, then that's a different issue - but still all the more reason for her to find information to help her manage life.
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