This study investigated the relationships between leader–member exchange (LMX) and workers’ perceptions of family–work conflict (FWC) and between LMX and satisfaction with remote working (SRW). It also assessed the moderating effect of employees’ ability to cope (AC) with the work in the interaction between LMX and FWC. Using a cross-sectional design, this study tested a moderated mediation model using Model 7 of Macro “PROCESS” for SPSS. The study sample consisted of 455 employees engaged in remote working activities during the COVID-19 health emergency. Surprisingly, the results showed that LMX was positively associated with FWC, while the latter was negatively associated with SWR. There were neither direct nor indirect effects of LMX on SRW, but the moderation of the AC with work on the relationship between LMX and FWC was significant and negative. In particular, the results showed that, in workers who reported lower values of AC, the increase in the quality of LMX also corresponded to an increase in FWC. Conversely, in employees with very high AC, as LMX increased, FWC decreased. Good relationships with the boss in a new and challenging situation such as remote working during COVID-19 threatens employees’ well-being when accompanied by poor coping skills. This study sheds light on these mechanisms and opens new questions in the literature about family–work conflict and remote working.