When we are depressed we can't 'see the wood for the trees', when, on top of that our previously secure world is uncertain or falling apart and all we see is a scary future, then we are in a dark wood and can't think logically or clearly enough to see a path out. Our fear paralyses us. We retreat further into our depression.
Please see your GP and start the process of recovery and that of getting support. Do you have any family or friends you can talk to? Contact the people you owe money to explain the situation if you haven't already. Speak to a debt advisory service.
Your children need you to find your inner strength. You DO have inner strength but I think your depression is creating such a sense of hopelessness that you are not in a position to take steps to help yourself. Which is why you need to get external support. If you haven't told family (or friends), perhaps through a sense of shame, embarassment or pride, now is the time to put those feelings aside. If you have potential sources of support - please speak to them. Sharing your situation and fears for the future will help. If you have a support network they will want to help you in any way they can.
You've taken a positive step by posting on here. You've reached out for help and now you know you can do that in real life. Facing up to your fears is hard but taking action helps you manage the situation and helps build up your inner strength to make the best of the situation. Whereas avoidance and retreating from it all cannot do anything but make things worse. I know this from experience. I think your feelings about your children have possibly come about through feelings of fear and failure and distancing yourself from them mentally is another way of of avoiding squaring up to the situation, and all possibly the result of being extremely depressed.
Your marriage is suffering and the arguments are to be expected but can you talk to your husband calmly about getting other support in real life? It is possible you are both feeling alone in your marriage and so are not supporting each other or feeling supported.
When we get help for our depression we are better able to help ourselves. Getting advice and support starts the process of moving on from helplessness and hopelessness, and whilst it won't magic your financial issues away you won't feel so isolated or alone. A little of the weight is lifted.
Please start by seeing your GP and if you have a wait to get standard appointments ask for a same day or next day appointment - don't hold back on the need to be seen as soon as possible.
And finally, hold your children - literally - give them a hug - and start to reconnect with them at the most basic level. I think it will comfort you and will definitely comfort them.
It sounds simplistic but depression is both mentally and physically isolating, in my experience. And a hug is one little positive experience in the midst of all feelings of hopelessness.