There is a dearth of knowledge on the emotional challenges content-area teachers in English-medium instruction (EMI) programmes face, and how they manage their emotions in their efforts to negotiate a top-down language policy. This paper examines the entangled emotional experiences of EMI content-area teachers in Nepal's school education. In contrast to a psychological approach to teachers' emotions, this article draws on sociocultural and ideological perspectives on emotions to unpack a connection between emotions, institutional language policies, language ideologies, identity, and teacher agency. The analysis of EMI teachers' emotional dynamics essentially identifies their emotions as 'entanglements,' reflecting the interconnectedness of emotions with other variables such as language ideology, identity, and agency in content-and-language-integrated education. The findings of this study showed that teachers' limited English proficiency led to negative emotions (e.g. anxiety, fear, frustration, and shame), stimulating them to use English-Nepali bilingualism as a creative strategy to manage their emotional challenges and also to exercise their agency in response to their students' needs. However, their translanguaging strategy -- which otherwise might have included the students' home language, Bhojpuri -- was restricted by hegemonic language ideologies. The findings show that multilingual teachers typically do not experience emotions in a vacuum but in response to other social phenomena. The paper supports the argument that teacher emotion management is not an apolitical process but is rather ideologically and discursively constructed and situated.