I think you need to approach this a bit differently OP. I don't think it's a horrible thing to expect your kitty to be clean, but there seem to be two issues here, IMO.
1. Runny poo. I've found that no matter what you feed them kittens will have runny poo occasionally. As long as it's not constant, or horribly smelly, ect I generally take a wait-and-see approach. Both my boys went through bouts of runny poo to one extent or another in their first year. They were fed raw for most of that time. So IMO, not diet related. It will happen, just accept it and keep an eye on it for signs of a more serious problem.
That being said a change in diet might be in order depending on what you're currently feeding anyways. Check out the Heath and Nutrition forum for feeding info.
2. Cleaning. I agree with the other posters that hijacking your kitten as soon as she's out of the box to wet her bum and wipe can easily create a problem. If you check out some of the other posts here you'll find that it's a LOT easier to cause a litter box issue than it is to fix one.
However, I can see another way to do this. Rather than hijacking her and wiping make it into a mutual grooming session. Get a warm damp cloth and take your kitten to a comfy spot. Snuggle her, and as you do use the cloth in quick small strokes, like another cat would do, to groom her all over. Always go in the direction the hair goes, from the front to the back. This IMO will be a bonding experience and is a lot more natural than a simple grab and wipe. It will also teach her to help clean herself since as you 'lick' her with the cloth she'll be inclined to do the same. Make sure you keep your motions smooth and relaxed, with kittens grooming naturally moves into play. Once you're done grooming take advantage of that for a fun play session. This way she's clean, you've had a snuggle, she learned to e gently restrained and examined all over, and she gets to play with you to burn off some energy.
I think this could become a really lovely ritual between you. I know I used to do this with Doran (who was my bottle baby) and now I'm him preferred snuggle/grooming spot. I still 'help' by gently wiping his face with my thumb, with the grain of his fur of course. He LOVES it when Mummy helps!