Chompers was there first and he is alpha cat and he knows it. However, he also knows the new cat is a female and although he will be aggressive with her, he probably will not actually hurt her. Females won't mate with you if you hurt the, you know. (It matters not if she is fixed. Male cats have certain limitations on their behavior when it comes to females.) She knows she is subordinate and that is the reason she sometimes picks the fight. She is showing him she will stand up for herself. Unless they are actually injuring one another and tearing out fur and drawing blood, let them settle the social issue between them. Two weeks is not a long time for them to negotiate their peace, but you have noticed they will cohabitate the sofa and are beginning to show some evidence of getting along. Give them time, at least two months. If you are afraid to leave them alone together when you are not home, lock her up in her original safe room until you get home and can supervise. But really, this new social system will take one to two months to settle between them. Just make sure you give them equal time and attention and show them they are both welcome in the home.
You should have separate litter pans for each and separate food and water for each to keep one (the dominant) from denying the required food, water and litter from the other.
You should have separate litter pans for each and separate food and water for each to keep one (the dominant) from denying the required food, water and litter from the other.