Since you have another rabbit, I assume that this one is spayed, so her new behavior can’t be chalked up to hormones.
Aspen chips are one of the safe litters for rabbits and a little nibble here and there would be okay, but you don’t want her to be actually consuming quantities of it. A litter screen might work for you. Put the aspen chips on the bottom of the litter box for absorbency and odor control, then put the screen over them, with the hay on top of the screen. Or you may want to try a heavier litter, such as aspen or pine pellets, which would make flipping the box more difficult. You could still use the screen with the heavier litter. Aspen chips don’t weigh much, so using them would make it easier for a rabbit to tip over a box.
If the chew sticks are safe ones, apple or willow, then it’s natural for rabbits to actually eat them. Some rabbits may just chew and leave the bits behind, while others will totally chew and consume them.
The litter screens are sold in the store here, by themselves (2 sizes) or with the litter box. Some people have fashioned their own screens.