With NFS the server takes care about the security. There are several levels and several security settings.
A level on the server is exporting it read-only. Which can not be changed on the client.
With NFS v3 the security is handled according the user id (number).
This means the userids on the client must be the same as on the server.
The root user on the client is handled differently. By default user "0" (root) is mapped to user "nobody" on the server. Which usually give no access to user root. Server settings can change this behavior.
In your case the user "dandy" needs to have the same userid on the client and server to let user "dandy" read-write to all files/dirs belonging to user "dandy" on the server.
With NFS v4 there are more security options, which can be set on the server.
By default it is the same as in NFS v3, plus some with "Kerberos" which is usually not used, because it needs additional know-how and configuration.
See man nfs
and man exports
Reminder: in a network environment you need security even if it takes additional effort.
Of course with the right settings on the server, you can disable all security and let everybody read-write, by adding this options on the server in the corresponding "exports" file (with your example):
NFS v3:
/volume1/Barry/Plex/tv2 *(rw,no_subtree_check,all_squash,anonid=0,anaongid=0)
NFS v4
/volume1/Barry/Plex/tv2 *(rw,sec=sys,no_subtree_check,all_squash,anonid=0,anaongid=0)
Be aware, this gives everybody who can mount it full read-write access as user "root".
On the client you can use (according your example):
sudo mount 192.168.1.74:/volume1/Barry/Plex/tv2 /mnt/plex/media/tv2
or in "/etc/fstab":
192.168.1.74:/volume1/Barry/Plex/tv2 /mnt/plex/media/tv2 nfs nofail,defaults,rw,user 0 0