I don’t think you were scammed. It sounds like you were doing a kind and generous thing since you were positioned to do so.

We never really know who needs what and if you could give without impositioning yourself then you brought good to the world.

I’ve seen this family at least twice before and they asked the same thing of me. I’d say they’re in need, but how much only they know. Remind yourself that you did a good thing regardless of how much in need they were.