Children's acquisition of filler-gap dependencies has been argued by some to depend on innate grammatical knowledge, while others suggest that the distributional evidence available in child-directed speech suffices. Unfortunately, the relevant input is difficult to quantify at scale with fine granularity, making this question difficult to resolve. We present a system that identifies three core filler-gap constructions in spoken English corpora -- matrix wh-questions, embedded wh-questions, and relative clauses -- and further identifies the extraction site (i.e., subject vs. object vs. adjunct). Our approach combines constituency and dependency parsing, leveraging their complementary strengths for construction classification and extraction site identification. We validate the system on human-annotated data and find that it scores well across most categories. Applying the system to 57 English CHILDES corpora, we are able to characterize children's filler-gap input and their filler-gap production trajectories over the course of development, including construction-specific frequencies and extraction-site asymmetries. The resulting fine-grained labels enable future work in both acquisition and computational studies, which we demonstrate with a case study using filtered corpus training with language models.