Difficulty accepting newly discovered half sister

Hi. I am in a state of emotional crisis after my mother's recent disclosure of having a daughter out of wedlock in 1970 and giving her up for adoption. I am 33 years old and was never told of this person's existence until she initiated contact with my mother. While my mom had previously decided to take this secret to her grave and never inform me or my full sister, she immediately began having near daily phone contact with this person, has visited her several times, calls adopted daughter's children her grandchildren. They only started having contact 3 months ago.I am struggling mightily to cope with and accept this situation. I was raised the first born child in my family and it has been an identity crisis of such to discover that there was another one before me. Also, my mother is very critical of my feelings of betrayal, sadness, fear that our relationship will never recover this situation. I am in therapy, but can't seem to work things out with my mom so that we can even talk about this without fighting. She tells me that I should be happy for her, and should just decide not to be upset any more. I can't just stuff my own feelings like that. I feel like she is cheating on me with another daughter and I can't find any source of support from others who may have gone through something similar. I am hoping that someone out there will see this and offer me some contructive advice as to how to mend my relationship with my mom and come to terms with this person who seems to be replacing me in my own family.