What is the ruling regarding my mother-in-law preferring her sister’s daughter over me, and her depriving me of help with household chores, knowing that this preference did not exist previously? And am I sinful if I use another entrance to my home to avoid passing through my mother-in-law’s house, while being careful not to sever ties with her and to greet her?

There is no blame upon your mother-in-law for exempting you from serving her and sufficing with the service of her niece; there is no offense to you in that. It is permissible for you to use the other entrance to the house to avoid passing by your mother-in-law, as long as you avoid severing ties. However, if passing by your mother-in-law's entrance does not harm you, it is preferable to please your husband and prevent disagreements. It is advised to be patient with your mother-in-law, to think well of her, to treat her kindly, and to overlook her shortcomings, seeking the countenance of Allah.