Lila is adorable and I hope that you can solve the problems you have now. All of the suggestions are good; I think a screen door would be ideal, althought you run the risk of those very sharp puppy nails destroying it in no time.
Do you have a garage where she could stay until she's housebroken?
My first two Goldens were very young puppies when they came home and, because of the way my house is designed, I was able to keep them in the kitchen, with the door to the dining room closed, while I was at work. I never used a crate. If you can keep her confined in a room where accidents wouldn't be a problem, it will make you and her much happier.