Between my partner and I, I'm almost always the bad cop. I'm the one with the "stern parent voice". It's important that our children understand what we're angry about (so I make it a pont to talk to them after I've calmed down) but it's equally important that they know there will be consequences for their actions. Of course when they were younger, I was quite lenient but now that they're much older (13 and 10) I find it necessary to let them know that small things you don't do right can lead to big things that are really wrong.
I think you're doing a great job in asking forgiveness from your kids but don't beat yourself too much about it. We're parents. It's our job to be parents. ☺