I would probably address with Alyssa that her grandfather may not be around much longer. Kids facing death, even if they don’t understand it well, can understand to some degree saying goodbye differently than ‘see ya next week!’ If my grampa had died when I was four (she’s four?) I think I would have resented them not addressing it with me beforehand. She may understand better than you think sometimes I think I understood death better as a child than I do now. Now I find myself flailing to wrap my head around it. I no longer expect to see my grandfather, but I have a hard time understanding ‘dead’.
It’s hard but we addressed with the boys that they may not be seeing one of our beloved pets again last week. She was dying and had to go for risky surgery, and is now recovering. We just sat them down and said ‘she might die. You might never get to see her again. You need to give her hugs and tell her you love her and whatever you want to tell her because you might not get another chance.’. They didn’t really get it, but we gave them a chance. One gave her a quick pet and the other a peck (they’re four and six). But I think it was better than telling them she went to some great farm

I’m sorry, Jenn. I’m sorry you have to deal with this. No one’s an expert, not even the ones with the degrees, because there’s just no ‘right’ way to grieve. I do hope you give Alyssa the chance to tell her great grandfather about her dolls or something important to her because she won’t get another chance.