Well, being overweight often goes along with stress and not sleeping well.
It's great that you have an active job. That activity will be helping your health. But weight is mostly about diet. I used to run for over three hours per day and was still overweight because I had a cake-making hobby!
I think that once you're feeling a bit better from getting enough sleep and getting proper exercise (stretching, strength, and cardio), you'll be in a better position to tackle the eating. For now, do what you can to eat only at defined meal times and to cut back on junk.
The reason I think you need to be getting other exercise even though you have an active job is that you'll still have muscle stiffness and tension. Also, even if you're walking around, you won't be building muscle (which is lost as we get older, particularly during menopause). Your heart rate probably isn't getting that elevated. If you feel stronger and fitter, you'll feel better in general.
I'm breaking my promise not to nag here... Please, please deal with your sleep issues. Make an appointment with your GP. If you can afford it, maybe find a specialist to talk to about it. Shift workers often have poor health and issues with depression, etc, because of the constantly disrupted sleep schedule. The exercise will help.
Things may not be great with your partner, but if you're going to have to keep living together, they can get better. It sounds like everything is getting on top of you and you need to do something to break out of that rut. I think working on the sleep and joining a gym/exercise class might be the key.
I lost weight when I went for an appointment for a hospital procedure and a very straight-talking surgeon asked if I knew how much I weighed. I told her a figure that was five stone less than I turned out to weigh! I came out of that appointment and immediately changed my ways. Three years later, I think I've only overeaten two or three times since. I count my calories so that I don't eat over a certain number each day and changed hobbies! I don't know how helpful this is for you but maybe it helps to know it can be done and it's OK to put yourself first and take all of these issues very seriously.
Tell your family you're not feeling great and need to make some changes. Maybe you can get the kids on board with eating more healthily and joining you in exercise. It would be nice to spend time with them away from a screen and doing something to teach them healthy habits. I really hope this works out for you.