Purely practical advice coming up: Crying everyday at work isn't normal. Nor is it very professional to be honest. You really should try to keep an unemotional facade on at work if you want to be taken seriously. Leave your family problems at the door and act, act, act - paste a smile on your face and be really upbeat and give the impression that everything is under control and you are a strong member of the team. This is particularly true if most of the team is male. Emotions freak them out at work. No-one will come and ask you advice if they think you are going to burst into tears. Harsh but true. I think you will soon find that people will start to treat you differently at work, and that will help you feel better about yourself.
Please don't think that I am belittling how you feel, I'm not at all, as I have been at work where I am falling apart inside. Its a horrible feeling.
If you really feel that you can't go on as you are, then I would spend some time preparing your CV , speak to some agencies, build up a strong LinkedIn profile, and start applying for some other roles. No job is worth being so miserable over. As my parents always told me, its easier to look for a job when you are in a job. Time is on your side at the moment.
Getting to work: If you only work 7 miles away, have you thought about cycling some or all of the way? Maybe a folding bike? You would feel better with some fresh air, you would probably get to and from work faster.
Could you work from home one day a week? I work from home. It does take discipline to ignore the household chores, but if you drop the kids at BC then come home, make a cup of tea, shut the door, switch off the phone, you will be amazed how productive you can be without interruptions. I often put a load of washing on before work. Hang it out in my lunch break and bring it in at the end of the day. (I'm not perfect: if I see the rain coming down I do run like a bat out of hell to get it in, working or not!)
With regards to your husband's attitude to you. Maybe you need to change how you respond to him. He may subconsciously find your job intimidating, maybe he feels that you consider your job more demanding than his (just a thought) and feels a little belittled and ignored? Maybe the next time he says that he's had a crap day too, you could ask him to tell you about it and see if there is anything you can do to help him. If you get a positive conversation started with him, you could then ask him if he has any advice for you.
Your OH may also be panicking inside: he knows that the household needs your income, but is terrified that you are about to be ill and lose your job. He may well be worried about you but doesn't know how to confront it. Maybe relationship counselling would be a good idea to open up the communication a bit.
Your kids really need to be at the forefront of all this. Are they suffering from your and your husband being so unhappy about this situation? No-one wants to grow up in a miserable house. What practical steps can you take to improve the situation for them? Star chart for being ready on time for school, with a monthly outing or reward. Mealtimes or a quiet time all together each evening with everyone telling a funny story or something that happened to them that day. Simple things can make a lot of difference.
Also, have you tried Mindfulness or CBT? I know it sounds very hippy, but I have seen proof that it works (my OH had a breakdown a few years ago and this was the way forward for him). You could ask your GP for a referral or there are some good podcasts that you can listen to.