Op- you are NOT a terrible mother, far from it. Life has got in the way that's all and you seem to have lost sight of you.
I won't pretend to say I understand your situation because I don't. However, i felt similar a few years ago and couldn't cope. I had mentally checked out ( sounds like you have too ) and went to see my doctor and was adamant that I wasn't taking any medication.
After a while I knew I needed some help so reluctantly took anti- depressants. There are many types and the term "anti-depressant" covers a vast amount of meds.
The ones I take are primarily for help with anxiety and OCD which I was subsequently diagnosed with. I wouldn't say I'm depressed, more like overwhelmed!
Anyway, the first few weeks were tough i won't lie, then I woke up one day and felt brighter. I started to find joy in things again, heard the birds singing and all that shite.... but truly I started to feel more like me again and still do.
Modern life with all of its conveniences is meant to be easier for us ( machine washes clothes, machine washes dishes, children have iPads to entertain themselves etc ) but I think there is so much bloody pressure on us to "perform" and be the perfect mum.
So what would you like to change if you had a magic wand? Truly? Would you like to be without the kids? I bet deep down you wouldn't but they need a serious bout of discipline, consequences and maybe watch a documentary with them that will open their eyes and feel immense gratitude for what they have. I did this with my now 8yr old dd who was becoming a spoilt brat ( the documentary is on YouTube and is called "poor kids" and features several children in the U.K. All around the ages of your dc who have very, very little ) and my dd was horrified and we had a good chat about how lucky she is.
You don't mention your age op, is a new career an option for you?
I sense your despair and recognise those feelings and honesty want you to know that it can get better. Ironically, my relationship was pretty good at the time I was at my lowest and now it's awful. I can see things much clearer and this year will very much be a make or break for us.
I would be happy to chat with you by pm if you want to, always helps to get things off your chest and even better to make a new friend 
Regardless though, I wish you loads of luck and hope you manage to get through today 