I think you're doing a great job so far. It's a huge success to have moved them indoors.
Your mom is not likely going to change overnight. But at least you have your Dad on your side, and with time, she may come around. Your Dad's a smart man: Lose the rats, and lose the daughter -- Keep the rats, and keep the daughter around a little longer LOL. See, they really do love you and want you to be around. But it will take a great deal of effort on your part to keep the cage and surroundings clean. I'm sure Mom wouldn't be pleased if she found poop on the laundry room floor.
Just be careful if your family uses powdered laundry detergent. If you're pouring haphazzardly (spelling?) into the washing machine, fine particles can go into the air and get into the rats lungs.
What are you doing with the soiled laundry? That could be what's causing the smell. If it's just sitting in a bin somewhere, that would def stink.
Just take it one step at a time. Your noodles is so cute, and looks like a cartoon character! How could any mother not love that face?