I need help resolving arguments!

First of all my husband and I have a 2 year old and a 1 year old, it's hard. We argue ALL THE TIME... But since we don't want to yell in front of kids, it's mostly like someone (him) pouting about something and not speaking to me. Today it occured to me that maybe I don't know how to resolve an argument. My siblings are way older and way younger than me, and I never had roommates. I do not know what to do when someone in my house is mad at me! Last night he was mad bc he wanted me to put our son to bed, I wanted to take our daughter, and then our son was incredibly annoying. I apologized after, said I would do bedtime tonight. I apologized again in the morning. Nothing. Mad at me all day. What do I do with that??