My kitchen drain has been draining slowly-so slow that I am unable to use dishwasher because of debris coming back into dishwasher. My husband (who is not a plumber) used a "snake" and also the thing that goes onto a water hose that swells then burst water into pipe. Nothing has worked. Now water is coming out from under slab just outside of kitchen door where drain runs. Now what? Please help?

water is coming out from under slab just outside of kitchen door where drain runs.
This puts the problem past the drain in the wall and in the line under the slab.
Snake from the kitchen roof vent.
Put out enough snake to reach the base and 18 feet more. Flush with a tub of hot water. Good luck, Tom