There is no substitute for being authentically "there" for them—for genuinely trying to help them resolve problems. For putting your relationship with them at the forefront of every interaction, whether it is playing together or working together.
None of us are perfect—we'll all have some regrets. But with my kids 19, 16, and 13, I can now say that I will never say anything like, "I wish I'd let them fight it out more," or "I wish I'd punished them more," or "I wish I'd yelled at them more." I will only ever say that I wish I'd been more patient, more attentive, more calm and accepting of the normal stresses of having young children.
One interaction at a time. Just make the next interaction a relationship-building one. Don't worry about the one AFTER that, until IT becomes "the next one."
photo by Sandra Dodd, of a 17th century dog