This has to be a very tough time for you, especially with kids. Asking for help is a good start.
Maybe if you provide a bit more info, others will chime in with helpful suggestions.
You found a place to live? Have a job? Your needs, goals?
As far as your credit the only thing you can do now is start the rebuilding process. You need to try to GW your creditors to try to get some of the lates removed. Also, you can try a secured card to get started again. You have to start building a positive payment history to outweigh the negative accounts.
It will take time to get to a decent score but I’m sure it’s possible.
honestly at this point, I would forget about rebuilding, and start stashing as much money away in savings as much as you possibly can, so you don't ever end up in that situation again.
Where's the dad? Is he paying any child support? If not, contact the state and they will start garnishment. If he's not working, then his future tax refunds for state and federal will go to back child support, and not him.
Rebuilding should not be your number one priority right now. You have kids and taking care of them and you are #1. Apply for local and federal support...food stamps, housing etc..Remember, its only temporary, and you don't ever want to be in a position again that you are depending on someone else like friends or family.
Get you own life together first, get at least 3 months at the minimum of an emergency Savings account that you don't touch, then you can tackle other aspects of your life.
Lates and CO AFTER a BK is even worse than just the BK, so forget it right now. Concentrate on you and your kids, and finding as much help and support locally as you can.