Tuppeny, I think your DP is being massively unreasonable.
Even though you have been to the GP and prescribed pills, even though you have explained to him how you are feeling and how stressful it is taking care of 3 young children, he is still working all hours (6 am to midnight on a sunday???) and blowing you off about a holiday. Okay fine, he has a deadline, you have to respect that, but if he really appreciated how awful you are feeling he should at least be helping make plans for how to improve things once this deadline is past.
I would be telling him that if he doesn't fancy a holiday, fine. YOU are going away for a few days on your own to get some sleep and a much-needed break, and he can stay home with the kids and see for himself how full-on it is.
I know you would rather have a nice family holiday but if he's just going to ruin that, then why push for it? Why set yourself up to be even more stressed?
Obviously you need to change some things for yourself, to make it easier for you to cope with the DC all day and things like that, but I feel like this thread is so much about what you have to do to make things better and not enough about how your DP needs to step up and make life easier for you too.
When is his deadline? I'd be making a deal to leave him in peace until then, let him focus on that, but with the understanding that the day after you will be coming up with a new plan together to do whatever is necessary to improve things.