If she is passing droppings, I would not worry. Chickens can and will swallow tablets. Calcium citrate with vitamin D tablets 300 to 600 mg can be put directly into her beak to swallow. Put it back into the beak and she will swallow it. Tums may be split in half and given the same way. The...
Sometimes the cloaca can come outside the vent slightly when they are straining, and then go back inside. Do you have any pictures of the vent? Do you have any calcium or Tums that you can give orally? They can swallow it. That can help with muscle contraction if one is trying to lay an egg.