In the larger installation kit there is a larger squeegee. Why would I need that? I am installing fill on windows roughly 28 inches wide by 14 inches high.

The small green card is designed for the initial smoothing of the film and the cuts around the edges. The larger squeegee is meant to be used to get all the soap and water removed during the final "press out" of the install process. If you watch the video below, it will show the intended uses. Some films are very sensitive and the small card can be a little rough for the surface, so wrapping a microfiber or soft paper towel around the edges can help prevent scratches. https://www.decorativefilm.com/installation-instructions