Ok, now I've read the other comments, I am back!
I sort of disagree with Crimson on the "manage the chaos".
That is a valid straegy (see my game, or the "Too much to carry" game); but I don't think that's the vibe you are going for.
This is closer to a chill idle game, which relies less on chaos and more on progression as I suggested (and, I now see, you were already thinking of).
You could do one or the other properly; but I don't recommend trying to put both in the same game.
I tried to "play" with the kittens; but it didn't seem to do anything, so I assumed mama could only play with the toys.
Maybe I was unlucky.
One final thing I remembered: have you tested if the kittens ever wake up if they aren't put in the bed?
The start screen said they "rest faster"; but I left one out to test how long it takes, and it didn't seem to ever wake up.