Dog barks at 4am and wakes up the whole neighborhood!?

My fiance and I recently moved in with my mother to save for a house. Our dog and my mother's dog are best friends. We used to live in an apartment and our dog was allowed to sleep in bed with us. She didn't have a yard so we walked her regularly. Since we've moved in, my mom doesn't allow the dogs upstairs so she is not allowed to sleep with us. She doesn't seem to have a problem with this. She has access to the living room, the kitchen, the laundry room and there is a dog door leading out to the 1 acre yard that she has access to 24/7. The problem is that she starts barking every morning between 4am and 5:30am. If she has access to the yard she goes out and barks at the birds and she is so loud we are afraid she is waking up the neighbors. If we close her in she starts barking at my mom's dog because she wants to play and then we don't get much sleep. What should we do? What is the best way to train her? Im afraid that by going downstairs to scold her I am actually reinforcing the bad behavior by showing up whenever she barks.