MangoBiscuit has it right - for most people its hard to do something positive for yourself when you feel worthless. Losing weight is an investment in yourself and requires you to feel like someone worth investing in. If you're filled with self loathing you will be stuck in a self defeating loop.
Added to that it's really hard to lose weight when seriously sleep deprived for three reasons - one is that sleep deprivation causes your cortisol levels to rise, which leads your body to hold on to fat reserves and your metabolism to slow, and the other is the instinct to reach for sugar to give you a short energy boost to "keep going" when really you need sleep (and of course the third is lack of energy to plan, shop for and cook healthy food instead of eating instant processed food).
Fedup12423 I think you need to concentrate on looking after yourself first - is there any way to get more sleep (is your DC's father living with you and can he take responsibility for ensuring that you gwt two nights per week uninterrupted, and you do the same for him, or if not can he start having them overnight once or twice per week now the youngest is 3? Otherwise is there a grandparent who might have dc3 one night per week short term?)
Buy yourself a few well fitting, inexpensive pieces of clothing so you can feel better now.
If practical - if their father is in the household to parent his kids - ring fence an hour per day just for you to go for a walk without the children. If you can't do it daily ring fence what time you can, even if its just once per week, for this.
Most people can't be shamed or insulted into losing weight - rather the opposite. Once you feel better in yourself it will be easy to lose weight, but while you're chronically tired and unhappy its near impossible.
I've lost seven stone over the last 13 months, but couldn't do it previously because of sleep deprivation (my youngest also didn't sleep, woke every 90 minutes until he was 3, then once he stopped waking me every 90 minutes I started a shift work job and then studying simultaneously, I just took too much on) and stress. It was easy to lose the weight once other aspects of my life became easier. You have to sort your mindset and sleep out first, seriously.

