WHAT DO IT MEAN TO SIGN A WAIVER OF NOTICE OF PROBATE OF WILL?

Waiver of Notice of Probate means that you know that the probate has started. If you do not sign they will have to notify you by certified mail. I would consult with another local probate attorney who can advise you on local customs with regard to co-executors. It sounds like your sister may want you out of the picture.

Signing the Waiver of Notice of Probate is sensible as it eliminates the time and expense otherwise needed to send you notice by certified mail. This is notice of what you already know -- the Will has been probated. On the Co-Executor issue, I suggest you propose that your sister declines to serve so that you may be the sole Executor. See how the attorney responds to that! The Court does not ususally express a preference. The court's (Judge's) job is to oversee that the terms of the Will are carried out properly and that the Estate is administered correctly I find the reason asserted by the attorney to be suspect. The time is NOW for you to consult with an attorney of your choosing.

What it means is you need to consult a separate lawyer to figure out your rights. The lawyer asking you to sign the form obviously represents your sister.