Very sorry about your loss. Only you and your family will know everybody involved and what's best. I would definitely talk with both children about it, as this is/will be a new experience for them, whether they come along or not, to help them understand what is happening.
I don't know if you remember your own childhood experiences with death, I have couple of very clear memories from mine, starting chronologically:
When I was little (probably 4 onwards), I remember (and have since experienced many children being) quite matter of fact about death. Growing up in the countryside, there were the odd dead mice, birds, frogs etc around, which were my first encounters with death. I remember my parents explaining that they were dead and wouldn't fly/run around anymore (I can't quite remember how they put it). My way of dealing with it was to bury them carefully under the bushes in the garden, because it didn't feel right to just leave them lying on the road.
My favourite aunt died from cancer when I was about 12, we weren't allowed to visit her in hospital, and I am still sad that I never got to say good bye to her. No doubt it seemed the right thing for the adults making these decisions at the time, as they were wanting to "spare us". I recently talked about this with my mum, she hadn't realised how I felt about it. We children were taken along to the funeral, though, and I can still "see" the church, with the coffin covered in beautiful flowers, and everybody walking past the grave. It left a big impression, being the first funeral I had ever been to. But it felt right that we were there, from my 12-year old perspective, and allowed to say good bye to her. My youngest sibling was about 7 at the time.
All the best,
T