I'm so sorry you are faced with this distressing situation. It's not that unusual, actually for things like this to happen. You were smart to ask your vet for advice.
(Have you made sure that the little girl's paw is not hurting her? Usually stepping on a cat's foot does not hurt them, but I thought I would mention it anyway.)
Keep the feliway going, rub a little rescue remedy on their little faces every day, and treat the whole thing as a new cat introduction.
Set up a room for one cat. Food, litter and all. Have one kitty living in that room for a few days, and the other in the rest of the house. Don't discourage contact with paws under doors but keep them separate otherwise. Every other day change around, put the other kitty in the room and let the first kitty have the rest of the house.
In the mean time exchange smells by rubbing a shirt you have slept in on one cat then the other. Use two shirts so after you blend the smells for each cat you can put a shirt under each cat's dishes, so they associate the other cat's smell, blended with your and hers/his with good things.
After a week, attempt an introduction. Do it in a room that has sufficient elevated space for two cats. See how this introduction goes.
You can also, in addition, try the vanilla trick. Place a dot of vanilla on the nose, chin and root of tail of both cats to cause them to smell alike to one another. This levels the playing field.
In general, even after the re-introduction, make sure you have at least three litter boxes, with at least one of them in an area separate from the others. Make sure you have sufficient elevated space in every room, and also other cat favored spots, such as a cardboard box, and a box fort or two.
Welcome to the forum, and please keep us posted!
PS The rescue remedy is good for you, too.