As others have said - don’t beat yourself up. Perhaps it was your inner strength or the grace you received in the Sacraments earlier in the day, but it’s important to note that even though you went off on them, it didn’t progress further.
You may want to use the experience as an opportunity to teach the children and for personal growth. I’ve found with my children and others, a parent admitting they were wrong and asking forgiveness goes a long way to how children handle issues with their peers.
Pray for increased patience - remembering in order to develop the muscle you must continue to lift heavier weights and so in becoming more patient, your patience will be tested more.
When our kids start to escalate, I pull the car off the road and, if it’s a safe area, turn the car off, get out, and stand outside the car. If it’s the first time, the kids will wonder what you are doing (and probably stop fighting). I’ve found, after a time, my saying I was going to pull the car over and get out signaled the kids that I was about to loose it and they stopped fighting - at least long enough to get home.
Yes, they still argue, but they’ve learned that we will only tolerate so much and in certain places. Otherwise (if it’s a safe place) we will walk away and/or impose consequences.
…Think how fondly you will remember these years when they become parents themselves - or priests and religious trying to help parents through these years…