If an apology falls on deaf ears, do you still have to apologize?

So yesterday morning when I got the boys up I thought I'd try apologizing for acting the way I did the night before.  I wanted to tell them it's hard to have a lot of patience all the time and that at the end of the day that patience gets thinner and thinner and when I have to do tasks I really dislike it puts me in a rotten mood and I took it out on them but also Cooper you shouldn't have hit your brother but I shouldn't have reacted like that and I'm soooo sorry.

Yes, I really wanted to say all that, but I knew they would just stare at me and probably at the end of my diatribe they would just say "okay."

So I decided to take an easier, less dramatic route.  I waited until they were a few bites into their breakfast and then I said "sorry I was such a crab last night.  You get double goodnight kisses tonight."

Chewing their waffles, they looked up at me and Cooper says "okay."  I don't think Carson looked up.

Seriously, are apologies to my kids more for me than for them?  Do they really care?

I did feel better having said it to them, and maybe in ten years they'll remember their mom wasn't too good to tell them I'm sorry.

But just in case they never remember that, I showed up at the school to have lunch with them.  Maybe they'll never understand why I was there on that day, but for whatever reason they make a big deal about it when I surprise them at lunchtime.  And that's just fine with me...