Please place carts onto the character position whenever the character teleports (hearthing, going through a door, stairs, cave, minehole, ...) so the character can walk out of it without getting blocked by the cart.
Similar please for leashed animals, for these the addition of a 10 second timer where they're astounded by the new surroundings and being busy looking around (so they won't move unless being pulled by the leash) would be helpful.
Yes, it might look a bit strange - but stuff getting in the way by random (or worse, going up a minehole that is walled on the upper level with a cart that then spawns on the outside of that wall, runs toward the character, stops at the obstacle and getting detached on the other side of the wall) is unfun.