If you are on the PC version, which I'm assuming with multiple companions that you are, you can disable/enable the "angry" companion.
To do this:
1. open the console (~),
2. click on the companion, you'll get a code listed at the top center of the console,
3. type "disable" and hit enter,
4. exit console (~),
5. wait for the other companion to relax,
6. reopen console,
7. type "enable" and hit enter.
Note: Be sure that you've clicked on the companion and not some other element in the world. If your companion didn't disappear when you typed disable, immediately type enable and then retry to click on the companion, you may have to get closer.
This is good for if you don't have a calm spell or a means to cycle a loading screen.