have name - can't make contact

I am an adult adoptee in my 50s. Mom is in her 70s. A few years back I decided to attempt a search. I kept hitting dead end after dead end. Extremely frustrating and I felt the, consider my/her age, the clock was "ticking." Started to get a bit desperate and engaged the services of a professional. I know how may people feel about these services - I see your position. I did what I felt I had to do. A few months ago they gave me a name that was "100%" accurate. Based on connections on Ancestry DNA, the pieces all fit. I decided the best way to make contact was by phone. Seems she lives with her adult daughter (different Bfather). I decided to call during the day when she would be home alone (her daughter would be at work). That's where things all fell apart. No one answers the phone and there didn't seem to be a machine. I called various times during the day - about 6 times over a two week period. No answer each time. Especially frustrating considering how difficult it was to dial the number each time. Finally, someone answered the phone. I asked to speak with the person by name. I was asked "Can you call right back?" Odd request, but what the heck. I hung up, waited 30 seconds and dialed again. This time, someone else answered - apparently the daughter. Not very friendly at all. She said she lived with her mother, but gave no indication that the mother was home and did not offer to put her on the phone. I told her this was a personal call (as opposed to a telemarketer) and I knew her mother from way back. She told me she would tell her mother to call me back... but never offered to take a callback number. I had to ask her to take it, which she did very begrudgingly and with no small amount of attitude. This made me fairly certain the message was never delivered. Even it if was, it would have no meaning as I gave my real (adopted) name. Of course, I never heard back. I considered writing a letter. Based on my best guesses, I am 99% certain the same daughter will open the letter. I would like to avoid that situation. I have found sisters/brothers of my BMom. Trying to reach them has become a similar surreal experience. A sister that I thought would be easy to contact turns out to have a disconnected phone number. I'm sure I found her older brother and called his number today. A man answered and I stated "Hi, I'm trying to reach xxx." He responded with odd yelling noises and then hung up the phone. I had always thought the problem would be "what to say" when I made contact. All this work to finally have a name, address and phone number and I can't get anyone to speak to. The whole situation is odd. Look like I am back to the letter scenario. As I am sure that the daughter will "intercept" it, I think getting to the point is even more crucial. It is just hard to write something without any bitterness when I know the daughter is going to read it. There's likely something strange going on in that family, but I still can't hep taking the whole thing a little personal. My "last resort" effort is to send a letter via Fedex - that will let me know that it arrived and who signed for it. I would spell out who I am and that I have been trying to make contact. Any ideas or advice? Better ways of going about this? How I should approach the letter? Thanks in advance.