You maybe need to get a finer grain litter until she, and her paws, are a bit bigger though they all tend to track some litter out of the litter tray onto the floor.
She shouldn't be getting the poo stuck unless it is softer than it should be? Maybe if the litter grain is too big it doesn't coat/cover the poo properly?
Some cats do well with sand in their litter trays as its very fine, will probably still get onto your carpet though