Oh wow, you definitely did what you could and it's great that you see her. It sounds like the home is where she needs to be right now because the people there are trained to take care of her illness.
When my ex's grandpa was in a home he felt the same way, whenever we would go to visit we didn't stay too long because he said it drained him watching this man he loved just slipping away more each day. He wasn't the same person either, but he still went to see him to let him know he had love surrounding him. Your exhaustion is understanding but it's so amazing that your mom has you in her life
And being rested is best for your soul, it helps you take better care of yourself and your loved ones :) Glad you can get some sleep now.