I have had lots of experience with this, as I used to work at a fairly large shelter. 1st, remember the kitten is a baby also and has to go potty the min. it wakes up or after playing or eating! Just like a toddler that is being potty trained, the kitten probably does not know it has to go until it "HAS to GO"! It is best to keep puppies and kittens in a confined area when you are not with them.. like an old pack n Play with a piece of cardboard over the top, or a bathroom or laundry room. Their bed, some toys, a potty area (NO scoopable litter for kittens!!) and non-tipping food and water dishes.
Also, most shelters won't even adopt our puppies or kittens to families w/ children under 4 or 5. Young children often do not understand the difference between a stuffed kitty and a real one. They sit on the one, why can't they sit on the other?? They usually do not know that screaming and crying means pain..and often they just get very excited at the noise and increase the activity that is causing it..you know, like the toys that scream when you flop them on the floor??
So, try not to leave the toddler and kitten unattended AT ANY Time...so that when you are there, you can teach her 'easy' and 'gentle'. If you put the time and effort into this so that they build a loving relationship, full of respect for each other, they will be best friends forever. However, if the baby gets bitten or scratched, remember, the kitty was probably just trying to protect itself.
Hope this helps..