I think that what stands out for me from your OP is that you find that you can't really enjoy your days off with your toddler. Which makes the whole idea of pt teaching pointless. If you are tired and miserable anyway, what's the point?
I was a teacher (primary SLT with class responsibility) and, in the last couple of years I was doing it, found myself perilously close to burnout. Constantly stressed, pounding heart, pains in my chest and stomach, finding it harder and harder to generate those good lesson ideas... I found maternity leave a blissful relief and an absolute rest-cure; I was suddenly 'myself' again. To cut a long story short I ended up not returning to teaching. I got a new job (office based) and have never looked back.
The problem with solutions such as the OP switching to a different school or sector is that pt positions would be hard to find and she is likely to lose salary anyway by that move, as teachers no longer carry their positions on the pay spine with them. I calculated that although my new salary was less than my pay on the leadership spine, it was fairly similar to what I would have got by switching to another mainscale teaching post, especially as I would have lost my entitlement to UPS by moving school.
The other thing you might want to consider is, whether or not you want to take a second maternity leave? Obviously that is a personal matter, but it might be a factor in your plans.
If you don't, my plan in your shoes would be:
Hand in your notice next Monday - see if school come back with any changes to persuade you to stay (this is not un-common in my experience), or perhaps the offer of supply work. Make sure you put 31st Dec as your leaving date, so that you are paid until the end of that month.
Tell school that you are leaving teaching and ask if there are any other posts coming up - admin, SEN support? Might be worth considering. Perhaps a slight loss of face for a couple of days, but oh so worth it.
Immediately begin job hunting
Don't ask permission from your DH - you could be waiting forever. Sorry, but I don't think he is very supportive (or perhaps enjoys being difficult
) so the idea of coming to a supportive mutual agreement as you might with other partners is pie-in-the-sky. You have to just do or you will be stuck like this for the foreseeable future. I suspect that once he sees you happily settled in something else then there won't be a problem.
A few ideas:
Look at ideas for home working - search on MN for posts on earning money at home
Sessional work at your local FE college - if you teach maths or English they will snap you up. This could be in the evenings, a couple of times a week.
School admin roles?
University - known to be quite family friendly
Local council - also family friendly
Fundamentally, you just need something to tide you over while you take a breath and think about your longer term direction.