Hi K.,
My daughter was 3 when this story happened . . . I was driving her to daycare one day and she saw a cemetary. she asked what it was. I whispered a quick, "Give me words, Lord", and started out. I told her that when people got old and their bodies didn't work anymore, then God gave them new ones. The new ones don't get sick or break, or anything, but with the new one, you can't live here on earth, you have to live in God's house.
About 6 months later, my grandmother died. When I told my daughter about it, she thought for a little while, then said, "MOMMY!!! She doesn't need her wheelchair anymore !!!!" And she was VERY excited, because Grandma could now run and jump, just like she could.
I wrote a children's book using that as the story line, but no one bought it. :-) So, I give it to you, to share with your daughter.
The key is to be okay with the sorry and sadness, because WE will miss Grandma, and it does hurt, and sometimes it hurts WAY TOO MUCH. But, you also want your daughter to be impressed with God's love, and how when our bodies don't work anymore, He, in his love, provides a new and better one that never needs repair. And if you need things to do when she misses Grandma, maybe she can color a picture for her, and put it on the refrig. Or draw a picture of Grandma having fun in heaven. (It'll be interesting to see what "having fun in heaven" means to a 3 yr old, wouldn't it?)
The traumatic part of telling your daughter, is that in some ways, YOU are traumatized. It's so hard to face when Mom dies. Even if she was suffering, even if she was in a nursing home. She as Mom, and somehow when Mom dies, it's like we lose the opportunity to "run home to mom" and be a little kid again on the inside. But you know what? My dad died when I was only 1, and My mom never remarried. Whenever we as a family talked about Dad, we ALL cried. (sometimes we'd get my mom to share stories), but we weren't traumatized by that. We knew Dad was in heaven, and it was okay, because we also knew that while he lived he loved us dearly. And that's okay. I think you'll find that your daughter's faith will comfort you -- even at age 3.
Blessings, and peace. God is with you, too, even while being with your mom.