I am the executer of my mums will although there is some money and a house to sell as it is all going through probate the family who will get a share want to see mums bank statements can they do this

Your question is whether an heir has the right to see financial statements - and the answer is no, but... the probate process is public, so anybody (not just heirs) has the right to review the assets that are in the estate, and in most (all?) states you must provide an accounting of the estate to all interested parties, meaning all heirs and close relatives. They will get the full details, eventually, and so you could refuse the request from the heirs to see the actual bank statements and tell them to wait for an accounting of assets as you go through the probate process.