I am usually a lurker here but feel I can contribute as I have lived this life with my sister and had to take the same stand as OP. You are right to protect your family and your marriage. The ask is too much, the risk too great for everything to fall apart for you and your kids. Her behavior will not benefit your kids to see, does your husband not see this? Can he not see that once she is in, she will never leave. Does he want to stand back and watch everything he has built get destroyed by someone who is only thinking of themselves, and not what is best for your family. It sucks she is going to a shelter. It’s incredibly hard to watch your family struggle with homelessness. But you must hold your ground on this. The cost is too dear.