Re: dinneky doon
I've never heard of it and, as I'm sure you discovered, Google can shed no light on it either. If I remember, I'll ask my Irish friend next time I speak to her. The writer might have made it up.
The context means you can work out the meaning of the whole sentence - the woman believes that the solicitor will laugh the other person out of his office (refuse to represent them) and, if that doesn't happen, the woman will be extremely surprised.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.