We had major problems when one of mine was approx 5-6, and a new baby arrived. I suspect that the awful behaviour is essentially attention seeking - and we found a really quick way to reset the ‘default’ was in doing 1-to-1 days, where it rotates weekly, so each child gets to spend quality time just with one parent, and for the 5 year old, you should give them a lot of choice / agency / control over what they do, where they eat etc. So maybe give them a choice between 3 ‘special’ days out - and let them choose where you eat your lunch, and then give them a budget to choose a gift from the souvenir shop at the end of the day, for them, and for their sibling. And during the day, make sure to praise them, and boost their confidence.
We found, after one day of undivided attention, where they had quite a lot of control over where to go and what to do, it was almost like a magic switch had been flipped - it was almost immediate after one session!
We carried on doing this for quite a while - each weekend, it would rotate (we had two boys of 8&6, and a baby), so dc1 would have a special day with me one weekend, (while dh looked after the other two, and still had a nice day out) then the following weekend it would switch around, so that each boy would get a special 1-to-1 day out with each parent, over the course of a month.
Also - you need to make sure you and your dh alternate downtime for you both - maybe making sure that each of you get a child-free morning either every weekend, or every fortnight.
And is there any chance you could increase childcare during the week for the 2 year old? To allow a bit of a break… How soon will they be starting the pre-school year? That could be a big change, and allow a bit more time for you to recover your energy.
I also think improving your sleep quality and quantity could help things - and also agree with pps about going to GP and getting help to improve your mood. I have recently accessed therapy through IAPT (NHS), and it was really helpful. And medication might be an option to explore. Good luck!