Hi,
It certainly sounds like a very stressful situation, for both you and her. I haven't experienced anywhere near the same situation as you but I have had depression for a few years and it played a part in the break-up of 4 year relationship, so I can sort of understand it from the other side of the coin.
Firstly, the fact that you are here asking for help is a great sign. It shows that u do understand depression is an illness and it can be cured. You are doing the right thing in trying to find ways to help. She is right in saying that "you don't understand", you don't, and you probably never will, but that is perfectly ok! Depressed people don't want to hear an arbitrary off hand comment like "i understand" even if you have had depresion urself you don't know the feelings and thoughts that are going on in the persons head at that time.
People with depression don't like to accept help, any kind thoughts or offers of help may be misconstrued or just turned into negative thoughts in their head. There is really nothing you can do to "cheer her day", acting happy, trying to listen to happier music etc. can make the person feel even worse if their in a really low mood.
Don't always try to get her to talk about her feelings, This can be seen like ur just trying to get at her and might make things worse. Instead just be supportive and talk to her about anything if she brings up something. Try to get out of the house more, i don't know what age the children are but maybe you could do something with them, or even just the two of you could go for walks, or go to the cinema rather than watch a movie at home. Depressed people often want to avoid the world and stay inside in a shell where the feel protected and comfortable. but being in a different environment will help.
Even trivial little things like a card, a note with a smiley face, flowers, small gifts might help. As long as they are presnted just as a random gift or to let them know you are thinking of them, not to just cheer them up.
Depression comes in waves and anything you do will probably be met with resisitance but be persistant, yet gentle. Don't force them to do something they REALLY don't want to do, it will only lead to an argument. It may take a long time for depression to pass but all the little things will eventually sink in.
Most importantly however, remember to look after yourself. It is a lot of pressure on you, ontop of your job. Try to get a break from the situation, even if it is just going to sit in the park for an hour by urself to clear your thoughts and relax. Is there any friends or anyone you can talk to in confidence about how your trying to deal with the situation?
Apart from that all I can say is do a google search for "help supporting my wife with depression" or something like that, there will be 1000's of other people out there in the same situation. I also think this website is very good and covers the main points:
Helping someone with depressionhope some of this helps,
keep well,
e
"Give me something good to die for to make it beautiful to live"