I'm very sorry for your loss.
At 2, i think she would have been fine. Now at 3, no way- she would NOT understand and i know it would freak her out a lot. Do you want her to go up, or can you just have your DH hang in the back with her while you go up, and then trade off? I think that you could just tell her that you won't be seeing her anymore and that this is a way to say goodbye. I don't think a 2 year old needs or would expect any more info than that. Did your child know her very well, would she recognize her? I think that might just be a bit much for them to take in and be able to comprehend. But it's a personal choice, every family and culture handles death differently. My personal thoughts are that I don't want to bring up death until she can fully understand it. I just don't want her to have irrational fears and be afraid if I can just wait to explain it when she can form thought out questions and we can have an honest, back and forth dialouge about it
First, I am so sorry for your loss. When DH's grandpa passed away, we did not take DD to the viewing/visitation that immediately preceded the funeral. DD saw her great grandpa frequently and we knew she would not understand. Instead we had my parents bring her right before the funeral started and had them wait until the casket was closed before we had her come up. We knew she would confused...but as you will see from the various responses, each child is different.
As to how we prepared her for his funeral and for the "permanency" of his absence....We explained that great grandpa had passed away. I highly recommend the following...please don't tell DC that she is sleeping, etc. If DC asks questions, I recommend not saying GG was sick (DC will think that when you are sick the same thing will happen to you or when s/he is sick it will happen to them). We explained exactly what happened. GGrandpa had a stroke, etc. Our DD will still make comments like Great Grandpa is all gone?, etc. "all gone" were her words not ours. We confirm and then talk a little bit about him.
Hope this helps and again, I am sorry about your grandma.
I am sorry for your loss.
I agree with some of the other posters - I would not let DS see an open casket. My grandma passed away when I was 3, and I still remember vividly the funeral. I was very upset by the fact that my dad cried and various other aspects. It was a closed casket, and I can only imagine an open casket would have been a lot worse. My first open casket experience was a friend of mine when I was 15, and that was brutally upsetting. At 3, I think kids have all sorts of "typical" reactions. Some kids will be completely fine, some will be traumatized. I would err on the safe side and avoid them seeing the open casket. .