Looking for Adult Adpotee Friendships

I am an adoptee, aged 54 that has been looking on and off for my birth mother since 93. I have her name and age, and the few things my Mom told me many years ago before she died in 89. What drove me what that my Mom told me I had a brother 18 months older. I can't tell you all the efforts I have gone through to find this women. Recently, with all the ancestry.com ads, and being able to do DNA testing to find out my nationality. So I now believe I found her, along with 2 brothers. Literally 20 minutes from where I used to live. I passed over her name so many times because in 95 I had an attorney/friend write a letter to her because the name sort of matched and figured to try. It was a beautiful letter saying we wanted to know if she had give a girl up for adoption, I did not want to interfere with her life, but to thank her for giving me the gift of life, and we wanted any information and whatever she was willing to give. She denied it was her. I believed her, so for 20 plus years, everytime her name came up, I said it's not her, I already tried her. I have used 2 different search companies, hours and hours of research. A week ago, a investigator who is a friend of a friend dug around, and again her name. with the data that is now available, it can only be her, and there is a brother 18 months older than me, and a younger half brother 12 years younger than me. So she is now 77, and the brothers are 56 and 42 with families of there own. I see their profiles on FB, and some of the pictures of especially the one brother and myself there are many similarities. One of the nieces has many of the same pictures of my son. I had my husband (who has a wonderful british accent - he really is british) call her so to have an intermediary. The whole conversation lasted 20 seconds. He asked if she was the person we were looking for and said he was helping his wife look for her blood family - he didn't even say birth mother - she said I have only two sons very angrily and hung up the phone. So she has rejected me now a third time. The other night I had a whole meltdown about all this. I have always wanted a sibling. My kids would love uncles and 1st cousins. They have none as my ex husband was an only child as well. Confused about what to do. I really don't want to harass a 77 year old that clearly wants nothing to do with this, but I truly believe my brothers don't even know I exist. I would like to somehow introduce me into their lives. However, the fear of more rejection has me paralyzed to do anything. Thank God I don't live near them as 18 years ago I moved my family 600 miles away from where I was born.Suggestions anyone.