Changing your weight and appearance (and most importantly, how you feel about your body) can't be done by dieting especially considering the kind of erratic eating behaviours you describe. And I'll be very honest, you are unlikely to ever have continuing positive feelings about your body while you continue as you are. The lifestyle you describe does not lend itself to feeling good about yourself.
You need to do two things and you can do them right now.
One: Make a GP appointment to have a blood work up. Check for any physical deficiencies that you make need supplementation or even medication for. Nutritional or hormonal deficiencies are a common cause of depression and anxiety, so if you need supplementation you could find yourself feeling significantly better before you know it.
Two: Decide right now to change your diet for good. Do you know what eating pattern makes you feel best? Personally I need at least 3 meals a day. A really, really good breakfast. A filling dinner mid afternoon. And an evening meal that is as big or small as my body dictates at the time. But always something, even if it's as small, a banana and a glass of milk. I also eat fruit and veg as snacks throughout the day whenever I feel the need. I'm starting a relatively physical mainly outdoors job soon, and I know from experience that I'll be adding some sort carb/protein snack to that around noon. Work out what meal pattern is best for you and commit to it. Then commit to eating fresh and healthy foods as much as possible.
If you eat a lot of processed sugar, cut it out completely for a while. (This includes alcohol.) Not forever but it's an insanely addictive food and you need to break the addiction to reset your appetite. It will take a few months but you'll feel better for not being beholden to an addiction and instead back in touch with your body. Be careful of artificial sweeteners. There is emerging evidence to show they make us hungrier as they trigger a redundant insulin response. Eat all the fruit you want and ignore nonsense about naturally occurring sugars in fruit. Our bodies react completely differently to an apple than they do to a chocolate digestive. If you like sweet, eat fruit.
Consider if you are eating too much simple carbohydrates. I don't hold to cutting out a necessary food group but most people with sedentary lifestyles eat too many carbs. One substantial helping of simple carbs like rice/potatoes/pasta with dinner along with all the carbs in fruit and veg are enough for people who don't do a lot of physical activity. Replace them with filling, health proteins like eggs and full fat dairy. Avoid low fat dairy, as it's nothing more than a source of extra, needless sugar and not as filling. If you eat dairy, eat full fat and as natural as you can get.
See the doctor and change your diet. Decide that as of now you are someone who eats sensibly and healthily. This is not a diet, not a fad, but your new lifestyle. The only part that's temporary is to avoid unhealthy treats until your new lifestyle feels ingrained. Then you can add chocolate/cake/alcohol or whatever back in on an occasional basis. Being mindful to cut it out for a week or so if you start craving again. You won't see immediate changes but just be having a steady eating pattern you will feel better before too long. And bit by bit you should see positive body changes.
Thirdly there is the final step. Physical activity. Personally, pushing myself into an exercise routine wouldn't work. I'm too lazy and/or too busy to exercise for exercise's sake. But this year I took up skating as an ongoing hobby. I love to skate. I will make sacrifices in order to be able to skate. I will never prioritise a netflix binge watch over a chance to skate. I'll never waste an hour on the internet if it's time I could have skated for. I have become insanely strong and fit by accident. I would never skate or do any exercise in order to get fit, but a by product of my hobby is increasing fitness. I've also reached a stage where that fitness has improved my skating, so I will now stay fit in order to maintain my skating ability when I can't skate. It's a lovely version of a vicious circle. So find your skating. It's not easy as a working parent but find something physical that you love. That you need to do for the love of it rather than as a bid to change your body. Then body changes are just gravy. And even more than that, your pride in the body that lets you achieve in the thing you love will change how you feel about your body. It's no longer about how it looks but about the mazing things it can do for you.