family issues - I really need some advice

Lynn
Hi everyone. I really some advice. Here's the story:
At the end of May my husband was offered a job in his home state (we were living across the country near my parents at the time). It was the opportunity of a lifetime for him but they only gave us two weeks to move across the country. At the time he was offered the position we were visiting his family in his home state. We had very little time to get back and pack and leave...I had to tell my parents and sister (they knew about the interview) but I knew they would be devestated. So I did something really dumb...
I sent out group text to them. It stated he had gotten the job and they gave us a very limited time frame. My train of thought was due to the time difference I would text them right away to let them know and then they would be able to call me as soon as one of them got off work.
Well that didn't happen. Immediately my mom started texting me bashing his family. My dad and sister never responded back. It wasn't until we were on our way back across the country that finally my mom picked up the phone. She was very very upset. Which is understandable. But we made a decision that was best for our family and there was nothing that could change it now.
We got back, packed up, and left. My sister came by one time to say bye (which was brief) and the my parents the night we left. 
We arrived back in my husband's home state and my family didn't talk to us to a solid two weeks. My mom started coming around after that and "forgave me for what I had done" and my dad maybe three months after that.
My sister however has not forgiven me. I told me mom a couple months ago that I felt like my family had disowned me for moving and texting that we were moving. She told me she spoke with both my dad and sister and said they did not feel that way. My sister still wasn't really talking to me but I felt better about it.
Fast forward to three weeks ago. I'm on fb and I noticed my cousin who lives a couple hours from me tagged my sister in a photo. I quickly called my mom and asked if my sister was on my side of the country. She said yes, she had flown in to an airport to visit some friends that were about 8 hrs away from me. I told her about her being tagged on fb and that she was only 5 hrs away not 8.
So I called my sister and asked her what was going on. She stated she didn't want to tell me she was in my state because it was a last minute thing and she didn't want to upset me. She then told me she would be less than 3 hrs away on staturday and maybe we could meet for lunch. 
I was so hurt. I balled my eyes out for the next couple of hours trying to decide if I would go have lunch. I decided that I would. 
I drove 3 hrs that Saturday to have lunch with her. I get to the restaurant and two of her life long friends were there too. She didn't get up to hug me, just said hi. She barely spoke to me the whole lunch. Her friend was the only one who engaged in a conversation with me. I'd ask my sister questions about her life, job, dog etc and i would only get one word answers. She didn't ask me one question about my life, new job, house, nothing.
Then her friend let it slip that she has a new boyfriend. If looks could kill her friend would have went up in flames. I thought my sister was going to throw her margarita at her.
She mentions that they're heading into town to go shopping and I can come with. So I do but I had to tail behind them. The sidewalk isn't wide enough and they were engrossed in their own convo. I'm the older sibling and I seriously felt like the younger sibling tagging along. 
Then I left. Drove another 3 hrs home. 
I also figured out the trip wasn't last minute. She had this planned and I was not part of the plan. If my cousin hadn't tagged her on fb she would have went back to her side of the country and never said anything.
So how's its been three weeks and she still isn't speaking to me. My mom told me today she is still hurt over me texting her I'm moving and then moving....
I don't know what to do! I've apologized, I've reached out, I met her for lunch! 
I was thinking about writing her a letter apologizing again. 
What do you guys think??? 
What would you do?