I think you need to do both:
- see what can be changed at work to reduce your workload/make it more manageable/carve out work-free times
- talk to your DH about how you both see/desire things to work out in the short/mid/long term.
Regarding the second, I think it is important though to acknowledge that most likely, any job that will give you satisfaction (unlike your previous job that made you unhappy) will have an initial time frame that will be rather full on. But that that is an investment that you probably do need to make in order to protect your long-term happiness prospects. Your DH is worried about your mental health, so presumably he does not want to see you stuck in a job for the rest of your life that makes you unhappy, either.
So whereas I would not (and did not) sacrifice family life for the sake of a job/career for ever, neither would I recommend to sacrifice your career prospects for ever for the sake of your family life (which is kind of what I did do). Instead, look at your job carefully, how it is now, how it will be in a year or two or three. Can you hold out until that first sabbatical? Can you and DH view the first three years in your new job as that mad time that you just need to get through, batten down the hatches, make it the family's priority, because it is highly likely that things will get better afterwards?
(BTW don't let anyone talk you into thinking that any particular three years in your children's lives are THE most essential ones for you to be around a lot.)
Because that is the thing about permanent lectureships. They're permanent. Once you have passed probation (what is it, three years?) it is very unlikely things will go wrong. Once those first manic years are behind you, not only will your work be easier (built up stock of lectures etc) but also you will have much more say in how much pressure you want to submit yourself to. And you will have that sabbatical too.
That is kind of what DP did. Walked into lectureship straight from PhD, quickly promoted to Senior Lecturer then Reader. Worked insanely hard for a few years, then relaxed into his permanent post and put all that 'excellency' stuff on the back burner, for the sake of our family and having time/flexibility for the kids. Especially his research output - he was still researching a lot, but not publishing as much. Did not make his department super happy of course... but that was kind of his 'career break' which he was able to take due to having a permanent post. Now that kids are a bit bigger - he is 10 years into his job - he has been picking up the pace again for the last couple of years, and he has a lot of research ready to be written up and submitted. But he could not have done that - taken a few years of 'down-time' - if he had not had that security of the permanent post.)
So take that into account when discussing with DH. No, your current work load is not sustainable, but (with some adjustments etc where possible) - is it doable, with the support from your whole family, for a few years? With the reward being a long-term happy 'you' in a permanent, rewarding post with career prospects.
Also, from my perspective I strongly advise you to REALLY consider the alternatives (again, jointly with your DH). If you drop out now (to do anything else really) then realistically, you will never reach that 'relative calm' in a permanent academic job. Whenever you think you'd like to go back onto the academic career track, you will be looking at at least a few manic first years to overcome first. Why would it be different if you tried again in a few years? (Especially as you probably wouldn't get anything like your job so easily again) So basically if you drop out now, you're out. Now if the choice really is 'eternal stress' vs. boring, unfulfilling job, then no, I wouldn't go for the eternal stress either, as it won't make you happy in the long term (just like the other job won't) but will stop you from spending time with your family on top of the unhappiness. But if the choice is 'hard draft for a few years' vs 'forever being stuck in a job that makes you unhappy' then (in discussion with DH) I'd advise to stick it out. (Whilst making any adjustments at work, as have been suggested on the thread, that will hopefully enable you to have a slightly more sustainable/manageable workload, of course).
Finally, a PP speculated that you got that permanent senior lectureship due to it basically being in a crap university. If that is the case, then do take that PPs advice to heart, it makes a lot of sense. However I'm thinking it may alternatively be possible that you are a highflier - very notable, successful PhD, probably a few papers published already, top of the 'year' at a first-rate university. And perhaps in a subject where there is slightly less competition (e.g. economics, where a significant proportion of PhDs choose to go into much better paying non-academic jobs).
If that's the case, that you are basically a superstar PhD (which got you that job) - then a) you may very well be putting too much pressure on yourself. You are accustomed to always being the best, always wow-ing everyone. You feel that with the senior lectureship come high expectations and you don't want to disappoint. In that case you need to let go of your perfectionism and relax into the 'good enough'. It's that or leave altogether isn't it?! You say in the OP that you want to do the job right or not at all, but is good enough - even only just good enough - not better than not at all?
And b) If you are such a 'born academic' then I think you would really regret leaving academia behind/forgoing that academic career.
I say all this as someone who never finished that PhD (when I had kids) despite everyone I knew thinking I was the born academic, including leading professors in my field. To get back into academia I would have to start a new PhD from scratch which would be much harder now than it would have been then to finish it. And just as I thought I was taking away too much time from my DS' first few years, I now hesitate to take time away from my DD's first few SCHOOL years. The time will never be right to go back so that's it for me, but I'm finding it hard to carve out a meaningful place in life outside of academia.