Activity recognition in children and infants is important in applications such as safety monitoring, behavior assessment, and child-robot interaction, among others. However, it differs from activity recognition in adults not only because body poses and proportions are different, but also because of the way in which actions are performed. This paper addresses the problem of infant action classification (up to 2 years old) in challenging conditions. The actions are performed in a pediatric rehabilitation environment in which not only infants but also robots and adults are present, with the infant being one of the smallest actors in the scene. We propose a multiview action classification system based on Faster R-CNN and LSTM networks, which fuses information from different views by using learnable fusion coefficients derived from detection confidence scores. The proposed system is view-independent, learns features that are close to view-invariant, and can handle new or missing views at test time. Our approach outperforms the state-of-the-art baseline model for this dataset by 11.4% in terms of average classification accuracy in four classes (crawl, sit, stand and walk). Moreover, experiments in a extended dataset from 6 subjects (8 to 24 months old) show that the proposed fusion strategy outperforms the best post-processing fusion strategy by 2.5% and 6.8% average classification accuracy in Leave One Super-session Out and Leave One Subject Out cross-validation, respectively.