No idea about unms built-in letsencrypt so can't help you with https://unms.mybusinessdomain.co.uk. When you use the 6443 port, you are bypassing the letsencrypt container and connecting directly to unifi, so no proper cert, only self signed, hence the warning message.
With regards to unifi.blah address, use the proxy conf for it, make sure you only have one active unifi conf, set the server name to that full unifi domain url. Also noticed that you changed your container name to "Unifi". That won't work as nginx won't resolve names with uppercase letters. Make sure your unifi container is named "unifi".
Just keep the unifi proxy conf default except for the server name directive.