Farewell, I was in the same position you were in at Easter last year - could not go on in my current job, could not face going down the grievance route and wanted to get out ASAP but with dignity.
I handed in my notice - it was 3 months and there was no opportunity to take holiday. I sent in a simple letter saying it was my intention to leave on xxxx date and that I was giving three months notice. That was it.
I didn't tell colleagues immediately, I let it filter out. When people asked me about it, I simply said that it was "time to move on, and look at other options." When they asked me if I had another job, I smiled and said "not yet." No one was under any misapprehension about why I was going - I was one in a long line of people leaving. But, by saying nothing much, I felt I kept dignity. When customers found out I was leaving, they asked why, I repeated the above.
As it happens I was offered a new, better job just as I worked my last day in the old one. But even if I hadn't been I would not have regretted my actions. The minute I handed in my notice I felt 100% better. My life changed completely, and I am a different person from the one I was last year. It is hard to reconclie yourself to this particular situation, with people saying "don't do it, do this instead, do that, they can't get away with it," etc, but you know yourself what you can handle - you have little children and other pressures - "it's only a job" is my new mantra; because it is.
I hope that you get everything sorted out to your satisfaction - whatever happens, you will manage - I felt that if I had to I would do any job for the money, and you can too.
Good luck