A.C.
I too have read some of your other posts & wonder if their fear of leaving the house is due to something more. If you're in town while this insulation is going on, why not visit the house? If you're not, ask a neighbor to take a photo or two every day or two so the kids can see their house is still there & the work that's going on. Take pictures of each child with each pet & put them in a folding frame (the kind that holds 2 pictures & folds like a book)-they'll be able to see them every day.
It took less than a month for us to have our house added on to when I was younger (once they had the foundation poured). Are you sure you're not being taken for a ride?