It can be heart breaking talking about Covid or its vaccine to loved ones if they simply don’t believe the wealth of official information available.
If their hesitancy or concerns cannot be satisfied by healthcare professionals, and their mindset is led by fake Covid news online, arguing with them will only further upset everyone involved.
One approach could be to suggest they fact check the reliability of the sources from where they’re getting their information. Ofcom, the UK's communications regulator, has a helpful website showing you how to recognise Covid misinformation as well as what to do about it.
https://www.ofcom.org.uk/research-and-data/media-literacy-research/coronavirus-resources