JumpJockey you sound exactly like me for most of the past four years. ds was a champion night-waker and also would never settle for dh, although he stopped at 19m we were in the middle of moving countries and I was 6m pg so I didn't get much sleep anyway - then dd came along and 2yrs in, she is STILL wanting to bf a couple of times a night. (and I never could express a full bottle, even if I'd had the time!)
I could never rest when the dc's went to bed either as I am an introvert and actually need some time on my own to process everything (mental, emotional) and recharge. I spent a good couple of years being ok with the dc's (just) but wanting to divorce dh approximately every 2nd day - displacement or what! Actually, seriously, I think it was a useful tactic, because it meant I was shirty with someone who (a) wasn't there most of the time and (b) could mostly take it when he was. (Of course, this only worked because even in that state I could recognise I didn't really want a divorce!) Instead I found the word itself to be a real red light - if 'divorce' started floating through my head too often, it was time for drastic action - by which I mean, I would go to bed at 10 a few nights running (it would take a couple of nights before going to bed = going to sleep instead of grinding my teeth). Because I was bfing I've been off caffeine; when the exhaustion got too much I did try a few grains of the real stuff in my decaf, but it made everything 10x worse.
when dd was 18m we had a go at sleep training but all we got was 10 days of 1-2hrs screaming a couple times a night and/or short screaming session + long fretty/whingey session. we tried again when she was 22m and she now sleeps til 4 most mornings (then bfs 3x before wake-up time, to make up for all she's missed
) Believe it or not getting to sleep through til 4 is a miracle for me - I am happier and able to be more responsive to both the dc's and my own warning signs.
which I realise is a LOT of wittering about me and not much help to you :) I think if you can just mainly be nice to your dc's - read with them, talk to them (I always found playing too hard - required too much brainspace + sitting still which made me fall sleep or nauseous trying not to) - and get through the move - for now, that will do. Once you get your nights sorted, even a little bit, as the others have said, everything will start to get easier.
ok poor dcs been waiting for their brekky - better go. good luck, hth a little.