Should I contact my half sister and how?

[Sockmate123]

I found out I had a half sister 12 years ago. She was a child at the time. I was expecting my first baby. She was the result of an affair my Dad had.
He had little contact with her other than sending money sporadically.
My Dad died 2 years ago. About 6 months after he died my mum received a letter from a solicitor saying my half sister would like to make contact with myself and my sister.
Sister and Mum were horrified and said absolutely not etc, didn't reply to the letter and destroyed it.
I have been thinking alot over the last couple of years I would like to open some kind of contact.
I wondered would a solicitor act as an intermediary for me to send a letter. I dont want to give her my phone number or address at this point. I would also have to do this behind my Mums back which I don't like doing but I think it's unfair she effectively made this decision for me.

@Sweetheart7 , she has a younger brother and sister with me , I’ve never felt the need to talk about the other child as her birth dad abandoned her for the last 20 years.

@anyolddinosaur
At the least your family owe her the medical details she asked for.

I agree with this. Depending on how important the medical details are then the girl could try to contact some of the rest of the dads family and the whole secret could come out anyway.

Yikes!

Thanks everyone for the replies.

In an ideal world life wouldn't be so complicated. In an ideal world my Mum would accept that I have a natural curiosity and sense of duty to my little sister. I dont know if I mentioned she is 19 years my junior so she really is my little sister.
There is only 11 years between her and my son.
In an ideal world my 'full' sister would be upfront and straightforward about what she really wants and doesn't. As I mentioned before she is so hard to trust as she constantly lies.
In an ideal world I wouldn't have found this out by accident and that my Dad wouldn't have cheated on my lovely Mum in the first place and leave an almighty mess behind.
I hope one day, somehow I will be able to reach out to her without causing even more hurt to those I love.
My Dad wasn't a bad person but flawed, as most of us humans are. He had his own challenges in life. He did mention to me a couple of years before his death that he would meet up with her again if she wished.
Thank you all for really reading and trying to help with this dilemma. This site can get negative reviews but I have found great insights and help through posting about this.

It's so difficult but life will have a way of making things right in time. I hope x

All correct, but her immaturity isn’t exactly OP’s problem either, is it.

With people like that, the thing is they say they’ll break, but they never actually do. They want to whine and act the cry-bully, but when you coolly say you’re going to live your own life as you please, thanks very much, they always back down.