I'm so sorry about your grandmother.
My son just attended his first funeral on Saturday. He's 3 and 2 months. He went to a home childcare until he was 2 and had been back there a few times since. The caregiver's husband, whom my son knew well because he worked at home, had been in and out of the hospital for many months with a hip replacement followed by complications, and then he died. Coincidentally, my son had asked about dying a few weeks earlier. I told him that the soul, "the part that really IS the person," comes out and goes to be with God when the body stops working. I told him how Jesus said there are many rooms in God's house and He will get our rooms ready for us.
When I learned that John had died, I told my son about it and explained that there would be a church service "to say thank you to God for making John to be with us, and to say please take good care of him and please help us remember him." My son wanted to go. He asked if John's wife and daughter were sad and talked about John getting their rooms in God's house ready for them.
We did not go to the "viewing" (I don't care for open caskets) but I think it was helpful to my son's comprehension to see John's body during the funeral. We whispered together about how that was just the empty body and John's "self" was already with God. (Afterward he said the body looked "weird" and pale, and I agreed and told him how I was thinking a lot about John's face when he was alive so that that's what I'll remember.) Everyone had a turn to walk up to the front, give condolences to the family, and view the body. My son was surprised to see John's wife crying (he hugged her) and even more surprised when I started crying as we returned to our seats. I explained that I felt bad for her because I knew how horrible I would feel if my own partner died. At the very end, when the casket was closed and John's wife had to follow it out the door, she really broke down and sobbed and wailed. My son has asked about this over and over since, and I have been explaining that although she DOES know that they'll be together in God's house someday, that seems like a long time from now and she misses him in her house now; it will take her a while to get used to not having him around and to learn a different way of loving him now that they're apart. Although she DOES know that his body was not really "him", the idea of never seeing his body again is very sad for her. My son seems to understand, but these big ideas are hard to get his head around, so he needs to talk about them a lot.
So...I guess I'd advise including your children as much as you can but getting people who are less devastated than you are to do most of the caretaking so that you can grieve and rest as you need to do.
Could MIL bring the kids to the wake and take them home when they've had enough? Could she sit with them at the funeral? Then they'd be near you as much as possible, but you wouldn't be distracted with worrying over how they take it.
Dancing Mommy of 2: I would not take the kids to the funeral under the circumstances you describe. Maybe have them make sympathy cards for your sister's closest family.