Child-robot interaction (CRI) has been mostly studied in labs and classroom settings. In this work, we share a CRI language processing study carried out in children's homes, analyzing how each language processing layer performs with children at home with no researcher present. We carried out an experiment in two phases: a first iteration with 7 families in Spain cohabiting with a simulated robot for 2 weeks and a second iteration with 31 families: 11 in Spain, 9 in Ukraine and 11 in the USA completing 4 cohabitation weeks at each country. The total number of children involved in the experiments was 55, ranging from 5 to 13 years old. Our goal in this study is to evaluate the performance of voice recognition, language understanding and dialogue management when children interact with a robot at home. Our results indicate that dialogue management capabilities are becoming the key element in the language processing pipeline; they also denote that the dialogue engine should include mixed-initiative capabilities and show the relative usage of different common built-in intents.