It sounds like it could be grief to me. There are SO many things to grieve. Grief and stress. I don't remember your story. How long since divorce or separation? How many kids and how old?
I would suggest to start scaling back on kids activities. I find it grueling. It disrupts any attempt to normalize a schedule, interferes with homework, meals, and bedtime. When you have to keep going like that all day long every day it is exhausting and I find the routine and monotony of it drive me out of my mind. I know that may not be possible right now as they are in the midst of things but in the future I would limit them a bit--or get them involved in solutions like car pooling so you don't have to drive every time.
I find I have to be really gentle with myself. Treat myself like I would want a friend to. You have a lot on your plate. Divorce, move, new job etc are major stressful events even when they are desired events--if they weren't then it adds another layer. Have ytou seen those charts that give stress points to life events? You would score really high.
Do you get down time on weekends? Is the kid's dad involved?
And yeah, the stiff upper lip doesn't really cut it. You have to work through this stuff or it just goes into hiding. Some random suggestions:
1) Counseling. If you can afford it do it!
2) Anti-depressants. I'm not a huge fan in general, but found with myself that they helped me get back on track. They helped me get out of the hole and pick myself up. The natural stuff didn't cut it. I used for about 3-4 months, got off and could tell that it made some changes.
3) Journaling. Write all these thoughts down. The ugly stuff. Get it out and then write a page about what you are grateful for.
4) Self-care. Got to do something for yourself. Have you gotten a new hobby since the divorce? Need something for you.
5) Work on house. Figure out what would make it better for you. You can't change the size right now but what can make it feel like home?
6) Are the kids involved in household stuff?
It can be really overwhelming at times. Admit that to yourself. You are doing a lot. I've been in overwhelm before (and probably will be again!) but things are good now.