I would definitely crate train her. At two years old being in a crate all night wouldn't be too long. Also, I would put her in the crate during the day when no one is home to watch her, not just for the pooping, but for any other kind of mischief she couldn find to get into while unsupersivesed, just until you know how she is alone. BTW, welcome to the wonderful world of being a bully parent. Aren't they awesome?