Reddit mentions of Sammy in the Sky

So sorry to hear this, what a rough time for your family. You've already gotten some great suggestions here, I just wanted to add a few picture books that might resonate for your kids and help open up some discussion. For the 3yo, you might try Goodbye Mousie or The Goodbye Book, both very simple ways to introduce the concept of death. For all three kids, some good ones about dogs specifically are The Forever Dog, Sammy in the Sky, and I'll Always Love You. The Tenth Good Thing About Barney is about a cat, but also a beautiful story.

There have been a number of other posts around here about explaining death to young children which you might find helpful to read through, such as this one, this one, and this one. You might also check out this link and this link, as well as these activites. It will help if you can give them something actionable to do with their grief, making your pup's last days memorable and celebrating his life after he passes.

edit: You might also take a look at My Very Exciting, Sorta Scary, Big Move: A workbook for children moving to a new home - might be a good way to help them process big feelings surrounding both this and the upcoming move.