She may be refusing because you're offering too much. I give non eaters at least 7 days before offering again. Maybe before trying live you could wait and a week and see how she does? If she refuses that too I would try live.

A rat pup (or smaller) would be fine to leave in with her as it won't cause harm to the snake.

Some snakes transition to live/ft easily and some don't. I have a big girl who took f/t just a couple times when I got her and now refuses to take it now so she gets live. Then I have a spider who was only on live when I got her and now takes f/t every feeding. It depends on the snake.