Some seatbelt setups don't "catch" by jerking the seatbelt. Some of them are inertia based and only "catch" when the vehicle is deaccelerated suddenly.
You can jerk them all day long and nothing is going to happen, it is not a very good test b/c it will never "catch" using this method. There is also the possibility that if you bought the van used that it had already been in a wreck and the seatbelts were broken before you took ownership.
We have been in two major accidents in Dodge minivans and survived quite well. I'm am getting tired of negligent drivers not paying attention and running red lights to T-Bone us or Rear end us at Stop lights, there is little excuse for hitting someone from behind, especially when you have the responsibility of your family's life in your hands.
I am glad to hear your family is OK, please drive safely.