The solicitor presumably was simply the acting deputy coroner for the area in which your fathers death took place. As such, any death in that area would come before her/him.
There would appear to be no conflict involved between acting as a coroner at an inquest in your fathers death and the case your mother had taken. It seems, though, that that would have distressed her. So another coroner dealt with the inquest at your request.
I don't see any other issue here, there certainly is no wrongdoing on anyones behalf?