E.M.
I'm so sorry to hear about your situation. I hope you are able to find the support you need to get through this. It sounds like you are really depressed about your new state in life... working, separated, handling everything on your own. If you are not a regular church goer, this may sound really weird or sound like it's just another awkward thing to add to your list of tasks... however, I strongly suggest you go to church. I suggest you find a place where you feel welcome and recognise that the people there are not perfect. Many people at church are in need of help... whether it is for their behavior or their issues in life or problems they've over come...etc. Getting that little bit of time to relax while the kids are being cared for can be very rewarding. At the same time, you may meet a great group of people who are interested in helping you find your way through this tough time. Sunday School is where you'll feel like you are more than just one in the mass group. That is where the relationships build and the individual caring really comes into play. I think service is wonderful because it teaches you so much, but right now, you need to surround yourself with people who are interested in you and supporting you whether it is with kind words or actions.
Careful not to burden the group with a giant download of your problems. Just feel them out and ask for help. When it is time to pray about any issues you may be having, don't be afraid to speak up about your problems. Ask for strength to get through these days. Ask for guidance to find a routine that helps you and your kids enjoy each other and/or to find people who you can trust. Maybe you'll find some other people who can make recommendations to you. Amazing things happen when you ask for help. It just may be the support you need.
Good luck to you and take care. I think the most important part of your message was that you identified you feel like you are letting them down and you are feeling bad about not being there for them. That means you have your priorities right, you just need some help getting things worked out.
Liz