This isn't just putting on weight - you've also reduced your activity for such a period of time (most likely because the 'dieting' completely drained you at first, then as you got heavier, it got harder, add in sleepless nights and so on) that your muscles, heart and lungs - so overall strength and fitness - are weakened.
It takes a lot of energy to move yourself when your muscles are weak; it's hard work to hold yourself up, to try and keep your feet in correct alignment and move without it stressing your feet, ankles, knees, hips, lower back, mid back, neck, head...
Food
You're definitely going about it right in terms of not limiting things until the point at which you feel bad and then go for the high energy things, catastrophising and then continuing as 'well, I've ruined it all now' - you need to be able to look at what you eat dispassionately, without judgement and be able to see where you have made particular choices, what could have influenced them and how you could respond differently in the future.
Are there particular things where you could make changes easily right away? Full sugar drinks? Large amounts of bread, sugars? Do the foods you choose when feeling vulnerable have particular qualities and very high energy accompaniments? Are you actually eating things that you genuinely like to reward or comfort yourself, or are you having them because they 'should' be treats and in all honesty, if it weren't for somebody telling you that they were treats, you'd actually rather have something else - so the 'treats' aren't making you feel better or tasting right, meaning they can't satisfy the need, even if you eat more of them?
Physical Needs
It won't cause instant weight loss, but what does work is exercise - not to 'burn calories' or anything like that, but to strengthen your body, as when you're more physically comfortable, you are able to move more without pain. It can take your head out and away from unhappy thoughts, too, as there's no room for that when the most pressing thing in your head is you reaching rep 10.
What you would need to benefit most from exercise in my opinion (I'm down 25% bodyweight over the last two years) are the following;
Feet
- A pair of comfortable running shoes. Because they're well made (it's a very good idea to get them fitted at a running shop and buy 1 size larger than usual to give your toes room rather than scrunching them up) and you can remove the insoles to replace with
- A set of arch supports/heel cups/orthotics. Your feet are now put into the correct alignment so that your weight is more safely distributed (no rolling your foot inwards creating stress higher up). You'll find some aches and pains from the muscles now working differently, as some will be weaker than others - if your foot drops in, chances are your leg turns in, your knee rotates inwards, your hip is uneven, etc. Which means the tighter muscles aren't working so hard, but the weaker ones are having to catch up. But it'll improve.
- A pack of comfortable sports socks. It protects you from rubbing, blisters and fundamentally, comfortable feet makes for a far better time.
- Some big knickers. They're not pretty, but something without frills and lace that gives you full coverage and some support to your abdomen is essential to avoid chafing and general discomfort as you move.
- Zip up sports bra. You're not going to be bouncing around in a cardio session if you've got any sense, so not an expensive one, you just need them kept in one place without straps digging in.
- Pair of leggings. There are brands on Amazon with good compression that go up to XXXL (check the weight ranges).
- Couple of sports vest tops for freedom of movement/coolness.
- Something to put over when you get cooler.
You're now sorted for comfortable exercise.
What exercise? That depends upon you. If you can stretch to monthly gym membership (and your GP area doesn't offer free exercise referrals to get membership somewhere - and you have childcare for around an hour), I can promise you that you are nowhere near being a noticeably large person. And start gently - not hauling around barbells and kettlebells and doing heavy cardio classes - 10 mins steady rowing to warm up, 20 minutes doing machines with a view to strengthening your legs, hips, back, followed by a gentle warm down on a recumbent bike is plenty to start with. Yeah, people say heavy lifting gives the best results fastest, but it doesn't if you're going so heavy that you hurt yourself when you're putting your body weight + another 20kg on your already weak knees; when you're significantly overweight, it protects you from injury to do at least a proportion of exercise sitting down.
An alternative or second activity would be swimming. Again, it strengthens, improves fitness and prevents impact damage from your bodyweight. For that, you just need a comfortable swimming costume, towel, bag, shower gel, shampoo/conditioner and a padlock for the locker. NO children in there with you - it's impossible to exercise when there are small children to prevent from drowning and it's certainly not relaxing for mind or body.
30 minutes twice a week? Maybe three times? Maybe gradually increase it to 45 mins? Add in travelling time and you're getting 3+ hours a week time for you and your needs. Because you deserve time to put your health and wellbeing first.
As you get stronger, you're in less pain, you improve your fitness, you move more, you get stronger, and so on. And it becomes so much easier to make food choices on the basis of what your body needs (because you're taking time every week to listen to your body) rather than what emotions and popular culture tell you - like the trope of unhappy woman eats an entire tub of ice cream, great for Ben & Jerry's to get that into public consciousness, but not that great for the unhappy woman who isn't feeling any better afterwards, who might have found a punnet of strawberries and some yoghurt just as comforting without the accompanying extra 3800 kcals, sugar rush and crash, nausea and self hatred. And a craving for chips.
Like I said, I'm 25% down on body weight now. I'll lose more over time, but the benefits of exercise are far greater than focusing on weightloss alone; a 57" waist measurement down to 36" and the ability to sprint like I'm about to take down a gazelle on the savannah (and look smug as hell about it when I power past DP) is due to the exercise. And I really, really enjoy the food I eat, rather than worry about what I can't have or that I've had too much, etc.
It can be done. You can do it - and by doing it, I mean you can feel better, happier and have more energy.