You definitely are doing a good job if they aren't miserable and hiding in corners, withering away. It sucked that when my son was born, the social worker told me that it was her job to call child services because I slept for 8 hours straight in the hospital and am diagnosed with Borderline Personality Disorder and also showed strong signs of post-partem. She told me that they probably wouldn't follow up on it though, but it still bothered me.
I'm extremely lucky with my son. I have been blessed with people that are happy to watch him when I need a break... which I admit is a bit too much sometimes. I believe I would be fine even if they didn't watch him, but I would most likely steadily decline in mood until I was much like I was after he was born. I'd smile and play with him while he was awake, but I'd cry as he slept... it was awful.
It's good that you've told them that there's something going on with you instead of trying to hide it. I'm sure with proper warning and explanation there will be less of a chance that things will turn out badly. You describe them as joyous children, and you are definitely to thank for that.

Never forget that they love their mommy, no matter what. (My mother is always expressing concern that my son is more attached to her than he is me, but I don't worry because he yells "mommy" over and over when he can't see me, and at this exact moment he has his arm wrapped around mine as he's sleeping next to me.) Your children definitely wouldn't be better off if you were gone. They would be lost without you, I'm quite sure.