I wrote this originally as a comment but decided to elaborate on an answer, as I went way over the character limit.
Disclaimer: These are not long term solutions to fighting, nor a root cause, these are just suggestions to relax already present tension and relax your children to stop rivalry before it escalates.
In someplace with less space, such as a car or a grocery store, playing games is extremely distracting as this can help them forget any anger and frustrations. The Quiet Game, Eye Spy with my Little Eye, The alphabet game, Rock Paper Scissors Tournament, etc. Distractions are a huge part of solving conflicts with small children, as they have very short attention spans.
At home, Quiet Bonding Time is a potential defuser. It can help both girls feel closer to you and debunk any, "She's the favorite" type speeches.
In this method, One child goes to their space, whether that be their room, a treehouse (with a fenced yard) or a playroom. To play with their own toys or read a book or do whatever they want. The other one spends the time with you, doing crafts or playing cards, but just spending time with you. Then they switch. You can start with 15-mins at each but you can increase or decrease these times depending on how much free time you have on any given night. This can happen every night (even if it's 10 minutes each activity!) or once a week. The more often, the less rivalry there is likely to be.
However, you do need to identify the root cause. This may be jealousy, lack of proper communication, or simply boredome.