@FreeDuck,
Oh no, I'm so sorry, FreeDuck.
That's so hard on both levels. Losing your kitty and having to tell your kids about it.
I do think that you should give them the option to be included in the burial. Maybe find a nice box and some nice fabric and wrap the kitty in the fabric and then put her in the box. Tell them what happened, first, then give them the option to see her. (If they don't want to, they only see the box.) Then allow them to help plan the burial.
As for actually telling them, straightforward is probably best. Exactly what you already said. (You found her this morning, you were sad, you knew the last day of school was special so you decided not to say anything right away, she was such a sweet kitty, etc.)
Maybe give them some time when they come home to talk about their last day, get situated a bit, etc., before dropping the bomb. Unless it'd be obvious to them right away that she's not there?