If you are going to use 2 external disks, then it would be smarter to use 1 with Time Machine, and then use the 2nd with another backup utility.
That way you protect yourself from and bugs that may occur in one of the backup utilities.
I use multiple external disks for backup. I use Time Machine on 1. SuperDuper! (paid app) on another, and Carbon Copy Cloner (paid app) on a third.
Carbon Copy Cloner would be the most flexible in its ability to include or exclude files and folder trees you desire. Again, this is a paid app, but it is well respected, widely used and the author used to work for Apple.
SuperDuper! is also well respected, and it has personally saved me many times, when I had a PowerPC based Mac, that kept corrupting my boot disk, back on the 2005-2010 time frame.
I have never been sorry buying either of these apps. I also purchased a copy of Carbon Copy Cloner for my Mom’s Mac.
And Carbon Copy Cloner has the ability to backup over the network to another Mac’s external disk.
And if you are looking for cloud backup, then Arq might be an option.
https://www.arqbackup.com