You are ABSOLUTELY RIGHT!! Kittens do not need to be eating adult food. They need KITTEN food until they're at least 1 yr old!
Anytime you change the diet of a cat (or kitten), their tummies take a few days to adjust. This is normal.......just like humans who've been on a diet, then go "out" and eat a big meal.....their tummies REBEL BIG TIME!! I know this from experience! :-)
Also, the wet food will cause looser / runnier poop, because there's so much water in it. Set out a bowl of DRY KITTEN food, for her to "nibble" on throughout the day, and her poop should start to firm up. The more liquid that goes in, the more liquid comes out.....even in the poop!
As for getting it on her back feet, clean her litterbox asap, when she "goes", so that she isn't stepping in it. The deeper the litter, the less likely she'll be to get it on her feet.
It's good that you're taking her to the vet......in case she has worms or Coccidia. Coccidia sometimes acts like this, but is easily diagnosed and treated.
Enjoy your new baby................hope everything is ok.
50+yrs cats, kittens / "issues"