Wow, join the club! =) I only have one kid, and work part time, and I can't seem to keep my house clean either! For that matter, I can't seem to get it all clean at once! My husband is out of town a lot, so that doesn't help, but still, I've often had the same feelings of "How does everyone else keep everything so under control and clean and organized, etc.?". First thing is- you're not a failure just because you're not Martha Stewart. Martha Stewart isn't even Martha Stewart without having a huge staff to do everything for her.
A few things that you might find helpful:
Have some sort of a routine. It helps keep some order in your life, the kids respond well to it and know what to expect, and if things start going crazy, you can kind of get back on track easier.
Set small goals for each day- ones that you know you can accomplish. Don't plan to clean the whole house, cook dinner, do all the laundry, watch the kids, exercise, rake the leaves, and bake cookies all in the same day! It won't happen, and then you'll feel like a failure, when in reality, the kids were fed, clean, taken care of, and you probably did get some other things accomplished!
I've found that sometimes it is easier for me to make a cleaning schedule so that I just clean one thing a day (or two or whatever, depending on how small the task is). That way your house may not be completely spotless all at the same time, but it still hasn't gotten so bad by the time it is time to clean again. I also get more of my cleaning done after my daughter goes to bed and during her naptime than when she is awake.
Involve your kids in your activities. Have them help you with putting the laundry in the washer and dryer, putting the silverware in the dishwasher (and taking it out), folding washclothes, helping to stir something in the kitchen, wiping the mirror, etc. They will gain great life skills, feel a sense of accomplishment, and you will get things done while still spending time with your kid. It might take a little longer to do each task, but the rewards are so great! My daughter loves to help- she starting asking to help me before she was even 2! If your kids are older, you can divide up some of the chores to help teach them responsibility.
If you are feeling very depressed and worthless, and feel there is no hope after trying some of these things, please talk to your doctor and see if medication might help you.
You are not alone! I hope that encourages you and brings a smile to your face! =)