Why the Fight?

Today was the public school's first day of school, so I decided to take the kids to Chuck E Cheese's. K had been asking to go for a while now and we either didn't have the time or he got in trouble and we were unable to go. I was really excited about taking them today. I always look forward to seeing their faces when they get to do something they've really been wanting to do for a while.
I woke up this morning expecting today to be a wonderful day. We were finished with school by 8 a.m. and I was going to surprise the kids by treating them to pizza and playtime.
When we got to Chuck E Cheese's, the 2 oldest were so excited. K immediately took the tokens he had from the last time we were went and started playing games and L ran around touching and "playing" every game that someone wasn't on. Then, Ms. Alex showed up and L and her started "playing games" together. Shortly thereafter, the pizza arrived at the table and K obediently came and ate. L on the other hand took a little longer and then once she got to the table, she didn't want to sit. It took her a little longer to eat. After they finished their meal, they got down and spent the rest of their tokens and ended up winning 144 tickets, which was able to get K a rocket and L a sucker. All was right with the world.
UNTIL.... we got home! I don't think we were home 15 minutes when they started arguing, fighting, and screaming at one another. After unsuccessfully trying to calm them down, I told them it was nap time and the dreaded, "I HATE YOU!" came from my firstborn's mouth. At first I was a little taken back and didn't know what to do. I mean really! I just took him somewhere he had been asking to go because HE wanted to go. The ONLY reason I wanted to go was because he wanted to go. I really enjoy watching them have fun. I love having fun with them, so I honestly don't understand why he feels the need to be so disrespectful. Not only did the words he said hurt, but it made me angry. It made me so angry that he got disciplined like I haven't disciplined him in a while. I had stopped doing that because it didn't seem to make anything better, but actually made things worse sometimes. Now, I don't know. I feel bad for what I did, but luckily I was able to maintain some self-control and didn't do what actually went through my head at that moment.
I want my kids to be happy, but not at the expense of mistreating others and being disrespectful. I also want to be an example of what a loving mother is. A mother with mercy and grace, but still has boundaries and still gets respect. I know my kids are young and it's "just a phase", but at what age do people stop allowing that to be an excuse and start teaching responsibility. I know I'm not perfect, but sometimes I don't know if my best is good enough. Then I realize, God knows I'm good enough and it's Him I should be living for, not my kids or anyone else.
I know how much it hurts when my son tells me, " I hate you" or "I don't love you" or "You're not my mother." It's hard not to break down in tears and wonder what I'm doing wrong.
I can't begin to imagine the pain God suffers when His children not only ignore Him, but choose to believe He doesn't care. I'm grateful I have a merciful God that allows me to be imperfect, doesn't expect me to get it right every time and loves me anyway. I don't expect any of my children to be perfect. I know they can't always control their emotions or behaviors, but what kind of mom would I be if I didn't help them try? All 3 kids are taking a nap right now as I type this, but I can't seem to enjoy the "quiet" time.