Hugs for you. I'm sorry you're having a tough time.
With the mortgage don't just accept taking your name off.You and your children need a home. See a solicitor and get advice on what you are entitled too from the marital assets. Plus you need to be careful of the council deeming that you made yourself homeless.
The relationships board is a fantastic form of support with the practicalities of seperation as well as the emotional. You could start a thread or just read others if that's what you wanted. Things like money, documents and ensuring things are split fairly.
Can you explain the circumstances to your team and ask not to be discharged yet? You will cope and get through this, it might not feel that way but you can. That you're being discharged shows you've overcame difficulties and made progress in the past. It's normal that this feels like a big thing, anyone would agree, you can do this.
In the meantime I'm a fan of lists. Write what you need to arrange, solicitor, childcare, mh team and approach one by one. Baby steps, not one huge problem but more manageable jobs. Don't b shy of asking for help with the jobs. Ask a friend to help with childcare for example. Yourchild's nursery or school may have things in pplace that could help, after school clubs and sure start links.
for you. Stay strong, you can do it.