It doesn't happen a lot, but sadly, it does happen. I've held my share of dying kits and it never gets easier.
Grab a bunch of mom's pee shavings and rub them all over the kit and the other kit. Then put her back in with mom and stay close by and make sure everything is alright.
Don't do vanilla. That's just another strange smell right now with a wired mom and an injured kit. Make the smell familiar, not new.
Any time I want to foster a kit, they get a good rub in the dirty shavings and in they go.