Facilitate communication between them. A preschooler especially is still figuring out how to articulate feelings, wants, and needs, but a six year old isn't perfect either. (The hardest part of this is that you have to decipher what the true feeling/want/need is that underlies the argument!)
Try to redirect when you see a conflict beginning. This can be:
- a simple distraction (asking about something completely irrelevant to their conflict, like "what snack should we have" at home, or "how many bananas do you think we need" at the grocery store)
- a verbal warning to stop a trigger behavior ("stop poking your sister," "don't make rude faces," "that isn't your toy and you need to give it back")
- setting a limit if there's a sharing dispute ("you can play with the tablet for ten minutes, then it's your sister's turn")
- removing the object of contention if they won't get along ("since you could not agree on taking turns, nobody gets to play")
- enforcing a physical separation (at least a few feet so they can't reach each other — quite hard in a car, but is feasible in most other situations)
If one or both is tired/hungry, they will lose their temper significantly faster and be harder to calm down. But the quicker you can redirect, the less situations there should be that escalate into very serious fights (ones that risk damaging children, property, or your peace of mind).
One long-term idea that may help is defining and defending personal space. Sharing is hard for most kids, but it gets harder when there are few things they really feel is their very own — my sons share a room and have arguments about toys, clothes, and space that they'd never consider arguing about with their sister (who has her own room). The need to fight for these things are mine seems stronger when the personal space is smaller, and trespassing (even accidentally) will get a stronger reaction. If they share a room and toys, this gets more challenging — find ways to emphasize some things that are "just theirs" and help defend that personal space ("you know that this is your sister's [thing], please respect her property and ask permission if you want to borrow it"). Sharing is an important skill, but so is respecting ownership or right to privacy.
If there seems to be a lot of underlying resentment about inequitable treatment, be honest about differences that lead to different privileges and responsibilities.
Why does OlderSister get to watch that TV show / stay up later?!?
She's older and so she can do different things. But she also has to do more work around the house!
Why does YoungerSister not have to do homework / set the table?!?
She's younger and so she doesn't have as many responsibilities. But she also doesn't get to do some fun things that you can!