GS, good to see you sounding positive here.
WRT discipline -- don't beat yourself up and don't assume that you have somehow failed. Your home wasn't normal and you are in a different position from those mum acquaintances of yours who seemed to have it all down. You and your children were living with a tyrant and that makes a big difference to you and to the children.
[I am going to refer to DC1 as he/his/him just for the sake of not cluttering my post]
Luckily for you, you have an articulate and intelligent DC1 who is able to talk to you, and who trusts you enough to reveal his feelings to you. That is something you can build on.
I suspect since DC1 has been exposed to an adult with zero empathy towards his mum and siblings, and has been treated with no hint of empathy himself by H he will need to have his own natural empathy encouraged. He should be praised for acts of kindness and loving things he does with and for the others and for and with you.
(I do think this child needs counselling as others have suggested. But watch out for the child who doesn't talk as much and who tries to be 'good' and is quiet. The squeaky wheel isn't always the only one who needs oil. The child who absorbed the conditioning best often has issues just as complicated if not moreso than the one who rebelled. Rebellion can be a very positive thing in fact. The habit of submission is often a more difficult problem to overcome as you yourself have seen).
To establish team spirit, each child can have a consistent simple and age appropriate chore that they are responsible for be it keeping one area neat or emptying the waste paper bin or polishing something on a regular basis. When children live with a tyrant their self esteem takes a battering because the family is fragmented and often members are played against one another, and also because never knowing how well they are doing means children's self esteem takes a battering. (You have seen how your own self esteem was beaten down by H's unpredictability and how other values took second place to the need to pander to H this has been the children's experience too).
In order to start building a new dynamic in your family it would be a good idea to establish the concept of a family team with you and your children -- everyone contributing to the good of the team could be a goal, and you will probably be able to talk about this concept in a way DC1 understands. Being 'Team Family' helps the family that now exists with you as captain to draw together even though one member is conspicuously absent.
Team spirit provides a boost to the children's morale and will help them feel secure even though the former boss is now out of the picture. It's especially important for the new team to have team rituals that emphasise togetherness. Mealtimes are the obvious occasions when the team can really pull together and then enjoy the fruits of co-operation and everyone's participation can be celebrated for instance, 'Thank you DC1 for a neat table setting and for helping DC3 put the napkins out so patiently' can accomplish a lot if DC1 hears it regularly. 'Thank you DC2 for your help in drying the plates and for reminding me that the bin is full' etc... All children can help a little with meal preparation and with meal suggestions too. You can all sit down and plan meals for the upcoming week. You can decide with them what meal plans are reasonable. They will appreciate having a say it will give them confidence that their voices are heard in the new Team Family.
As the children become competent at tasks, you can praise them, smile, and thus in a quiet way remind them that they are accountable to you. Catching them being good is an excellent way to keep them reminded that they answer to you -- giving positive as well as negative feedback really helps them establish how they are doing in a healthy way.
As they develop competence their self esteem can rise up from the toilet. At the same time, you are the captain and you can give them a pep talk about teamwork when they predictably fall short of what you would like, get lazy about things, don't feel like helping out. Maybe each team member could have one opt out day and when that is cashed in they need to keep up their good work for the rest of the week...
Another team ritual that can be nice and positive is a family board game or movie night when you all gather together (with laundry all done together and lunches made for school by everyone). Family fun is important and the children will cherish fun times together. It will help bind you all into a unit and give them something to look forward to when they have been co-operative and kind to each other.
Above all, try to be consistent. If you are having a bad day and snap at them or get irritated, apologise and tell them you will try harder. They need to see a good example of an adult with boundaries who realises when she has transgressed and tries to make amends, is willing to talk about her own feelings.
Banish your guilt. The DCs will not benefit from that. If there are issues they have with you relating to former family life, listen and accept what they say and apologise, promise to do better. Tell them you are grateful they have told you about their feelings. Don't cry about it in front of them or put your pain on their backs. You need to find another adult (counsellor, etc) to help you with that.
I also recommend "How to Talk so Kids Will Listen and Listen so Kids Will Talk''.