The fluid inside the blisters is not contagious, and will not cause poison ivy if another child touches it. The "spreading" of poison ivy on one person that you are describing, is due to different factors. When the resin touches the skin or clothing it sticks there until it is washed off. Often, people do not know that they have touched poison ivy, and may end up spreading the resin to other parts of their body with their hands or their clothing over the next day, until they've washed their hands or taken a bath. Since the rash doesn't occur until two or three days later, it can appear as though successive crops of blisters are developing over a one or two day period, all from that same exposure to the resin of the poison ivy plant.
There are some things you can do to prevent poison ivy: First, know what the plant looks like, and try to avoid it; next, wear clothing that will protect the skin if you know you will be in area where poison ivy is present; and last, wash up well as soon as possible after coming in from being out in the woods, including washing of the clothing that you wore. The less time the resin sits on the skin, the milder the reaction is likely to be.