S.H.
P., please do not think that I do not understand how difficult this is or that I am speaking against you. I am going to be blunt, however, because it is important to see this situation in blunt terms.
Both of your daughters are extremely small. YOU ARE THE ONLY ADULT. It is absolutely and completely in your control and it is absolutely and completely your responsibility to protect the older child from your younger child. It is absolutely and completely your job to train your younger child to behave properly. There is NO excuse for allowing her to get away with this.
I have a strong willed little boy who would dominate his older sister IF I ALLOW it, and I do NOT. He has to learn to be fair and kind if he wants to get along in this world and I would be hurting his future if I did not make him learn. If he bullies his siste I tell him he has to be kind, I explain to him two options that are fair and he can pick (for example, "let sister have a turn with the toy or go to your room until you are ready to share.?) IF he does not pick while I count down from 5, I pick him up and take him to his room. He must stay there until he is ready to behave. If he says he is ready but does not behave, then he goes back to his room. He has cried himself to sleep exactly one time. Mostly he decides to share before I am through counting. He had to learn to do that because there were consequences for his actions.
If he cannot control his sorrow when he is in his room, I will take him a glass of water, rock him in a chair, hug and kiss him and explain to him why he is there and tell him again that if he wants to come out and play, he has to do what I am asking. Sister deserves kindness and he will show it to her or he will not be allowed to play.
You have to have patience and strength. You are the mother. You decide how everyone will behave or they will suffer the consequences. You carry out the consequences. (I NEVER hit my children, by the way. I teach them and give them space to understand the teachings and make their own decisions without hurting eachother or any one else).
I suggest taking a parenting class. Google "parenting classes in New York" and I am certain that you will come up with a variety. Or you can go to your local India association or other cultural center and find older women to befriend who can tell you what worked for them. You need a mentor and some guidance to help you get through this. That is OK. We all need help.
Good luck to you. You can do this.