Logically, a marriage goes through many phases, the first few important ones are the stage of passion, realization, rebellion and then stage of co-operation. In simple terms, once the initial festival atmosphere of marriage passes by, then the truth sets in about two real lives coming together, living together. In the first year, most of the arguments and fights happen. After this, the marriage stabilizes. Right now, I think your marriage is just gone through the realization stage, you have to tide over until you reach the stage of cooperation. It will happen, most of us have gone through these difficult times successfully without separation.
The bridegroom is attached to his parents, the newlywed wife is attached to hers, so the shift of the emotional bonding is always not easy. As an adult, she would also emphasize on her individuality, independence, and freedom as you would want to.
The new environment and the incident of your father's re-marriage would be seen in a different way by your wife and there would be chances that she would be looking down upon your mother.
Without being emotional, try and see what all mistakes have happened like you have listed the faults with her, there would also be faults from you and your mother's side.
Marriage is a two-way street, more of giving and taking, at times you would end up compromising more, at other times, it would be the opposite. Initially, try not to escalate things, allow the tense atmosphere to settle down, give it another three months. Have a chat with your mother and she would understand. Then have a discussion with your wife and see what she really wants. At times because of the close proximity among the three at home, there would some unsettled issues that would not be obvious at first glance.
Spend time with her, take her out for a dinner, a movie, a short holiday or a day trip. Both of you start respecting each other and the marriage, then you will understand each other better. Try not to take sides strongly during an argument between your mother and wife. Do not scold or use harsh language against her, in the presence of your mother or other family members. Find out what her interests and hobbies are and encourage her. Some woman is attached to pets, continuing education or working. In your case, see if this applies and move on positively.
Visit temples or religious place as a family, let your mother also, forget what has happened and slowly bond with your wife. If there are issues with the division of work at home, kitchen, and laundry, try to be fair and settle it if need be employ maids or house help.
Over a few months, you will realize that things are getting better and your marriage becomes stable. Married life, balancing time and dividing love and affection is not that easy, we need lots of patience and never to jump the gun.