There is a lot of wonderful advice in this thread!
Do you have a friend you can call and vent to? It really helped me through my divorce to call my best friend and babble. I was so frazzled that sometimes when she picked up the phone, I'd be like, "Oh hi! Uh - I can't remember why I called you... guess I'll call back when I do!"
My biggest piece of advice, though, is to divide up your personal belongings as soon as possible and move into a new space. Don't move by yourself - hiring people to help is cheaper than you would think (look on Craigslist.) Enlist friends and family to help you pack. And donate as much as you can to Goodwill.
Having friends help me move was a Godsend in my case. Every time I tried to pack by myself, I would just end up crying or staring off and thinking about the relationship and feeling so sad.
I've seen this with other friends who have divorced; it's not just me - the dividing up of all the little things in your household can be very emotional. I recently helped a friend clean out his house of all the things his spouse had left behind - they'd been divorced for two, but she had left so many things, even her wedding dress! He just couldn't do it himself. He felt so much better afterwards, and I swear his house seems brighter now (and certainly much less cluttered!) His houseplants are even doing better now (although maybe he just takes better care now that it's not such a mess.)
So even if you stay in the same space, have your friends help you divide up all the belongings and consider rearranging all the furniture at the very least.
You are starting a wonderful new life with your kids. Believe me, it really helps to purge your belongings and start in a fresh space. Being in a new space helps to reaffirm that. It's a bold and healthy symbolic action to take.
Hang in there!
Tui
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mental mosaic - pick up your pieces; make something pretty