‘There is nothing wrong with wanting to know more about your half-siblings but tread carefully.’
She left her husband and children to be with my father.

My mother was 18 when she married her first husband. She got married to get away from her parents, who were loving, but rather strict and old-fashioned (this was in the 1960s). While married to her first husband, she had three children. They were still very young when she met my father and left her family for him.
If this makes my mum sound callous, it isn’t meant to. She was still very young and, I think, besotted with my father, who could be charming and good fun. But he was also a difficult man and their marriage eventually ended. He has since died.
I learned of my mum’s first family when one of my half-siblings, a sister, came to live with us when I was a young child and she was a teenager. I don’t know if we would ever have been told otherwise. 
I learned later from relatives that for some years my mum tried to keep in touch with her first three children (I also have a younger brother from my mum’s second marriage), but any letters or presents she sent were returned unopened. Eventually, she must have had to make the heartbreaking decision to give up.
This has not been talked about openly within the family. I have no idea how much contact my half-sister has with her siblings and, to my knowledge, my mum has not seen them since she left. I realised early on that it was a subject considered off limits, though I did clumsily try to find out more when I was younger. 
I know nothing about my other half-siblings, apart from their names, and have never felt any real desire to meet them. However, neither have I any desire to have to contact them for the first time when mum has died or is very ill. She is in her 70s and, although in good health now, this could soon change. My brother and half-sister both shy away from conflict and I have always assumed it would be me who would be left to sort this out.