Oh OP, I really feel for you. Yes, it truly does get better, although I too wouldn't have believed that in my 40s. I was rock bottom, newly divorced with two young teenagers, desperately poor, thought I couldn't go on. Everything was a struggle and there were times when I wished I wasn't on this earth at all.
Honestly, teenagers grow up. While you're going through it, it feels like you have children forever, but amazingly they grow up, become independent, you worry less about them, they get part-time jobs, then leave home/go to Uni or whatever.
You become freer than you've ever been. You have more experience workwise so manage to change jobs, you start to meet new people and make friends you didn't have when you were married, and those friends become supportive and good fun. You might even have other romantic relationships, you can't imagine that now but it will happen if you want it.
Eventually I got a job which really paid a decent wage and (at the time) also gave me accommodation. I made a move across the country, gained new skills, started to do things like travelling as I had the freedom and salary to do that. I would never, ever in my lowest days have thought I could do so much, see so much or learn so much.
I am in my 60s now, my life has had many twists and turns since my 40s and I have lived, and worked in various parts of the country and abroad. I am happy and content both with my age, stage and position in life, I have good memories and a supportive friendship circle and lots of things that I still want to do.
I don't want this post to sound self congratulatory - I do apologise if it comes across that way - I just want to reassure you that things really do get better. I have told you the things I'd liked to have told my past self if I could have gone back in time....honestly, hold on in there, believe in yourself, keep going and you will be fine. Life will get better, truly, it really will.