Oh, my dear, you are overwrought. And overworked. And overwhelmed, and none of these things mean you are not a good mom.
But you simply have to have something to fill your own tank. It sounds as if you are running on fumes right now, and that will make you more tired, more cranky, and feel more down.
When you say "veg," once the child is in bed, do you mean watch TV? Is there something you can do to recharge that would take about as little energy, but that might make you feel better? A luxurious bubble bath? A phone call to a friend? Even a little exercise might help boost your endorphins and help your mood.
On weekends, I always set a timer. By noon on Saturday, everything but laundry has to be finished. I do the most important stuff first (bathrooms, etc.) and go from there. And when noon hits, I'm done. I sometimes add an hour or two after church on Sunday to do more, but only an hour or two. If I don't get the weekend to have some of my own time, I'm not ready for a full week on Monday.
Do all you can to take care of yourself every single day. Fill your own tank, and it will make everything else easier. Take care, and I wish you luck!