Place small pork shoulder in the slow cooker. Drizzle barbecue sauce, ketchup and yellow mustard over the pork. Season pork with kosher salt, pepper and garlic powder. Slow cook for 7-8 hours on low or 4-5 hours on high. The pork is done when tender and able to easily pull apart.
Pull pork apart. Add barbecue sauce and mix until combined.
Mix the coleslaw with mayonnaise, lemon juice, apple cider vinegar, salt and pepper.
Preheat oven to 350 degrees. Slice slider rolls in half.
Layer pork in a single layer on bottom half of the rolls. Place tops of the rolls over the coleslaw. Melt butter and grate garlic into melted butter. Baste on top of rolls.
Cover sliders with aluminum foil and bake for 15-20 minutes. Remove from oven.
Remove the top half of the rolls. Top pork layer with coleslaw. Cut sliders and serve immediately or save for later.