You asked, "I thought about faxing a copy or scanning the will into my computer and emailing a copy, would either of those options be satisfactory?"
If you have their email address, send them a nice email and ask which way they would prefer. It would be showing a gesture of cooperation on your part. Unless you are dealing with "irregular" people, this should be taken kindly. I'm guessing that they want to be sure that they are no longer involved as a beneficiary. I am also guessing that they are disappointed that your mother would leave grand daughter out of her will.
By weaknesses, I was referring to a do-it-yourself will that might not have been constructed properly.