It may be a case that your family are just unfamiliar with the brand AMD, which is not surprising seeing how so many TV adverts play the 'Intel jingle'.
But you can always try showing these prices:
AMD Ryzen 2600 retail version (I.e. comes with a stock cooler) - $120
Buy Used - Like New: AMD Ryzen 5 2nd Gen - RYZEN 5 2600 Pinnacle Ridge (Zen+) 6-Core 3.4 GHz (3.9 GHz Max Boost) Socket AM4 65W YD2600BBAFBOX Desktop Processor with fast shipping and top-rated customer service. Once you know, you Newegg!
www.newegg.com
MSI PRO B450M PRO-M2 motherboard - $75
Buy MSI PRO B450M PRO-M2 V2 AM4 AMD B450 SATA 6Gb/s USB 3.1 HDMI Micro ATX AMD Motherboard with fast shipping and top-rated customer service. Once you know, you Newegg!
www.newegg.com
CORSAIR Vengeance LPX 16GB DDR4 - $75
Buy CORSAIR Vengeance LPX 16GB (2 x 8GB) 288-Pin PC RAM DDR4 3200 (PC4 25600) Desktop Memory Model CMK16GX4M2B3200C16 with fast shipping and top-rated customer service. Once you know, you Newegg!
www.newegg.com
SAMSUNG 860 EVO Series 2.5" 1TB - $130
Buy SAMSUNG 860 EVO Series 2.5" 1TB SATA III V-NAND 3-bit MLC Internal Solid State Drive (SSD) MZ-76E1T0B/AM with fast shipping and top-rated customer service. Once you know, you Newegg!
www.newegg.com
So all in, that comes to $400, saving your family $100. Then show the nearest Intel equivalent, I.e. 6 core, 12 thread CPU 3.4 - 3.9 GHz.
Intel Core i7-6800K - $320
Buy Intel Core i7-6800K - Core i7 6th Gen Broadwell-E 6-Core 3.4 GHz LGA 2011-v3 140W Desktop Processor - BX80671I76800K with fast shipping and top-rated customer service. Once you know, you Newegg!
www.newegg.com
The rest of the items could be sourced for the Intel platform at the same price. Yes one can purchase a 6 core Intel CPU for less than $320:
Intel Core i5-9400F - $155
Buy Intel Core i5 9th Gen - Core i5-9400F Coffee Lake 6-Core 2.9 GHz (4.1 GHz Turbo) LGA 1151 (300 Series) 65W BX80684I59400F Desktop Processor Without Graphics with fast shipping and top-rated customer service. Once you know, you Newegg!
www.newegg.com
But it's still more money that the Ryzen 2600. Then to help show that a CPU that can cope with lots of threads is best for video editing, show them the following:
https://www.cgdirector.com/best-computer-for-video-editing/ - old but shows that more cores is better
https://www.techsiting.com/best-processors-for-video-editing/ - note the number of Ryzen chips suggested
Ultimately though, the people paying the bill get the final say, so if they want an Intel system, then that's what you'll have to go with. It'll be fine, of course, but not as good as using the 2600 (which is one of the best CPUs AMD have produced, for the money, for a very long time).