What is the ruling on using money collected to purchase daʿwah materials in one city, then spending some of it on the family, and then the person wishes to spend the remainder on daʿwah in another city after relocating?

Your disposal of the trust funds by spending them on your children constitutes a betrayal. Allah has commanded the return of trusts and warned against betrayal. You must repent to Allah and spend the same amount of money that was deposited for its intended purpose, which is distributing tapes, brochures, and booklets to the people of the neighborhood where you used to live. If the donors stipulated that the funds be spent in a specific neighborhood, then their condition must be adhered to. Otherwise, it is permissible to spend them for the benefit of your current village.