After Jason was gone, our nest was empty. Neither of us was still employed, so no one had to go to work. If you are employed, most employers will give you time off until after the memorial service is over. We were fortunate in that regard, but not everyone is so fortunate.
I have known two other mothers from churches I've attended who did still have children at home. One was able to function and help her children grieve with her. The other was totally unable to do anything. She was so stricken by her son's death in an accident that she could barely deal with her responsibility to help her other children, some of whom were still quite young, who were missing their brother. Hard as it might be, you need to keep life as normal as possible for your other children as far as schedules go. Try to have meals at regular times and keep bedtime constant. If you have bedtime rituals, try to keep them intact, even if you don't feel like it. Someone may help you with getting food on the table, but you need to join your family to eat with them. Your other children have never been parents and can't comprehend your loss. They will be wondering why you are paying so much attention to someone who isn't there anymore and not paying as much attention to them when they still are there. You may find yourself pushing them away emotionally at the time they most need your support.
If you can't sleep, ask your doctor for some sleeping pills to get you past the first couple of weeks. If you have no appetite, eat anyway and take stress vitamins. Make sure you eat fruits and vegetables and healthy food -- even if you have to have it brought in. Junk food and fast food won't give the nutrients your body needs. If your church and the neighbors aren't bringing you healthy food, try the take-out deli at your local supermarket. We have had good luck with Vons stores here in California, and they have some good salads at reasonable prices.
When you don't feel up to nuturing your children, sit down with them and tell them that you are missing their brother or sister very much and it makes your heart hurt. Ask them how they feel. By your example, let them know it's OK to be sad or to cry because you have lost someone you loved. Explain that not everyone feels their sorrow the same way. Some people want to talk about it and some don't. Some grieving people want to be with people all the time and some just want to be left alone. Let them know if they want to talk, you will listen.