You are only getting it 'wrong' if its having such a detrimental effect on you.
Things will be at there hardest with two preschoolers - they take so much time and effort and childcare is expensive. So things may not improve until they are both at school.
In the short term though, I would address getting the house in order. Just a bit at a time if that's all you have energy for and get the kids out of the house with one parent while the other makes some progress. Once you get on top of it and get a bit of a routine, it's much easier to stay on top of.
Long term you may have scope to take a sideways step into a similar but different job? Something more rewarding or not so full of drudge. (Which also may feel worse atm because being a parent to preschoolers can be thankless and monotonous too). Short term, can you find any little ways to make your days nicer? A walk at lunch, a special meal cooked together at the weekend, a hot bath and a book after a particularly shit day at work, a slice of cake and a coffee? Little things but whatever works for you can give you a little lift at least.
Is it time to see the GP to get your panic attacks under control? There are lots of resources online, books you can get to help you deal with this issue.
But basically, if I were you, I'd try and stop thinking that you are getting things wrong and accept that this is a hard, chaotic, difficult time for lots of people juggling small kids and working and that you are honestly doing just fine. Things will get easier in the next few years as they start school, get more independent and childcare costs decrease. You may go back full time which will obviously increase your family income too. Id give thought to, and write down, a short term plan of how you can improve the house (realistically with the time and money you have), how you can improve your working day and if theres any way you can make some savings so that you have a bit of cash to put towards something to look forward to, even if it's just a weekend break away. Then, I'd get together a longer term plan, where would you like to direct your career, what needs doing to the house over the next five years (again, realistically) and how can you improve incomings/outgoings so that things feel more manageable. Do you have a large mortgage, can you downsize, is it better for your overall family life if you live somewhere a bit cheaper etc.
Sorry, that was a total essay...I'm sitting on DSs floor waiting for him to fall asleep and got a bit carried away 
