Fixes the 'cannot push thing being pulled' bug and other weirdness.

code/game/atoms_movable.dm

@@ -223,8 +223,6 @@
 /atom/movable/proc/doMove(atom/destination)
 	. = FALSE
 	if(destination)
-		if(pulledby)
-			pulledby.stop_pulling()
 		var/atom/oldloc = loc
 		var/same_loc = oldloc == destination
 		var/area/old_area = get_area(oldloc)
@@ -255,6 +253,10 @@
 					continue
 				AM.Crossed(src, oldloc)
 
+		// Break pulling if we are too far to pull now.
+		if(pulledby && (pulledby.z != src.z || get_dist(pulledby, src) > 1))
+			pulledby.stop_pulling()
+
 		Moved(oldloc, NONE, TRUE)
 		. = TRUE
 

code/modules/mob/living/living.dm

@@ -177,7 +177,9 @@ default behaviour is:
 			for(var/obj/structure/window/win in get_step(AM,t))
 				now_pushing = 0
 				return
+
 		step(AM, t)
+
 		if(ishuman(AM) && AM:grabbed_by)
 			for(var/obj/item/weapon/grab/G in AM:grabbed_by)
 				step(G:assailant, get_dir(G:assailant, AM))
@@ -730,7 +732,6 @@ default behaviour is:
 	return
 
 /mob/living/Move(a, b, flag)
-
 	if (buckled && buckled.loc != a) //not updating position
 		if(istype(buckled, /mob))	//If you're buckled to a mob, a la slime things, keep on rolling.
 			return buckled.Move(a, b)
@@ -816,9 +817,12 @@ default behaviour is:
 											if(istype(location, /turf/simulated))
 												location.add_blood(M)
 
-					step(pulling, get_dir(pulling.loc, T))
-					if(t)
-						M.start_pulling(t)
+					if(get_dist(pulling.loc, T) > 1 || pulling.loc.z != T.z)
+						M.stop_pulling()
+					else
+						step(pulling, get_dir(pulling.loc, T))
+						if(t)
+							M.start_pulling(t)
 				else
 					if (pulling)
 						if (istype(pulling, /obj/structure/window))
@@ -826,8 +830,11 @@ default behaviour is:
 							if(W.is_fulltile())
 								for(var/obj/structure/window/win in get_step(pulling,get_dir(pulling.loc, T)))
 									stop_pulling()
-					if (pulling)
-						step(pulling, get_dir(pulling.loc, T))
+
+						if(get_dist(pulling.loc, T) > 1 || pulling.loc.z != T.z) // This is needed or else pulled objects can't get pushed away.
+							stop_pulling()
+						else
+							step(pulling, get_dir(pulling.loc, T))
 	else
 		stop_pulling()
 		. = ..()