There's no such thing as a 'reading of the will' nowadays, if there ever was.It only exists in plays and films, not real life.
The will is subject to probate. Once it is admitted to probate, that is accepted as genuine and the last known will,probate is granted and the executors can set about administering the estate in accordance with the will.On the grant of probate the will becomes a public document and you may see it.
As your father has died only recently, it's possible that probate has not yet been granted.You may apply to your local Probate Office for a general search to find when probate was granted and, if that shows that it hasn't been, for a standing search for you to be told when it is granted. The standing search is valid for six months.