Background: Palliative care is a challenging specialty, especially when it comes to caring for children with serious life-limiting conditions and supporting their families. Workers face significant challenges and experience major impacts on their wellbeing. We conducted a qualitative study to understand the sources of stress in the palliative care team, their work expectations, and how they can cope with the demands. Methods: We used an online questionnaire about the causes of stress, the impact of the COVID-19 pandemic and the ways in which support is needed in the workplace. Results: Of the 56 palliative care professionals who participated in the survey, 57.1% considered the main causes of stress to be high workload, difficult emotional burdens (55.4%) affecting their outlook on life (61.2%), the death of patients (46.4%), and communication with patients’ families (26.8%). The COVID-19 pandemic increased stress levels for the majority of respondents (89.3%). The need for specialised training (53.6%), support groups, psychological counselling and adapted organisational policies was highlighted. Conclusions: The study demonstrates the importance of understanding the needs of both paediatric and adult palliative care staff in order to provide optimal care and support their balance in this demanding area of the healthcare system.