Honey, you have MAJOR wife troubles. You don't have a wife, you have a 4th child to look after.
Things obviously need to change. Of course she tells her friends she has a great marriage - she has a man to support her, with her giving NOTHING in return. If she can't take care of the kids and the house while you're working 120 hours a week, time to look for a new job with less hours and downsize your life - smaller house, older cars, less vacations, whatever it takes to make sure your kids are properly taken care of. Or, take over the finances, and give her an allowance to live on, instead of letting her spend your entire paycheck. You're working to support her in this lifestyle and getting nothing back from her.
It does sound like she may be depressed. If she's not taking care of herself, the kids, or the house, she might be clinically depressed and need medical attention. The fact that you work such long hours has to rough on both of you. It could be that she's not happy with how things are either, but just doesn't know how to pull herself out of it. Maybe she'd prefer a smaller house and more time with you...
If divorce is not an option (good for you) then counseling is a must. If she wants to continue this life, then she needs to step up, be a real wife, and start taking care of her children. Right now she's neglecting them, and that's not fair to them. But if she's not willing to change at all, remember that even the Catholic church allows divorce in abusive situations - and what she's doing (or not doing) for your daughters borders on abuse.
Put your foot down and stop allowing her to walk all over you. She doesn't deserve what you've given her.