I also believe there’s someone waiting in the wings. He’s DARVOing like it’s his full time job!
Sadly, all the things he’s telling you, appear to be his shortcomings and failings, but he can’t see this! And he’s not even a good father either!
50/50 custody with the kids doing a week with you, then a week with him, would be excellent, although would of course impact on your benefit entitlements, so it may be better if you approach this as you having the kids for 9 days per fortnight and he has them for 7 days per fortnight, preferably with him having them at least one weekend.
Of course, it could work out better if he has them EVERY weekend, from Friday after school (so he does school pick up and will have to navigate his job accordingly) until Sunday midday one weekend (so you get to have fun with them too) and from Friday after school until Monday morning (he’ll have to drop them off but again, he needs to negotiate with his work, just like other single parents do!).
He might not like this plan, so make sure that it’s documented with your solicitor writing to him/his solicitor, because the courts will take a dim view of a parent saying they don’t want as much custody/weekends because he wants a “free” and single life to do whatever at weekends. You on the other hand, will come across as being very reasonable and wanting to ensure that you promote and foster good relationships between your DC and your STBXH.
Don’t make it easy for him and don’t allow him to DARVO. Just say “OK” and don’t argue, cry, ask him to come back. He’ll hate it that you don’t try to defend yourself.
Have a notebook and wrote every interaction down, date, time, what he said, etc. This will be useful later.
Finally, don’t allow him to see you’re upset! Start wearing makeup (if you don’t already), dye your hair a different colour (if you want too of course), basically always look like your best self, to show him that you’re not only managing the kids, but you’re living your best life!
EDIT: he is also responsible for half the rent until the lease is up. Make sure that if he defaults on the rent, it’s on his credit file, not yours. He might want to walk away, but he literally can’t leave you in the lurch as far as the rent goes. Plus, you might be able to get housing benefit and some kind of council tax rebate as well.