Don't Worry They'll Come Back After A Few Days.
That is not correct. I'm afraid the triplets won't be seen again. When one or both the parents die you will be able to choose one of the kids to inherit the house, so one of them might appear again, but not all three.
Even during the transition process, since the kids' ages are randomised, it is likely that they will no longer appear to be triplets on the adoption screens.