To preface, I am a little confused as to your description of the mistake on DE-111. Are you listed in paragraph 2? If not, where does your sister's name appear on the Petition.
Notwithstanding the above, if I understand the facts as presented, you have two options: amend or supplement. To amend the Petition, you would need to handwrite the word "Amended" before the word Petition on the DE-111 with the corrections and re-file with the Court. California Rules of Court ("CRC") 7.104. However, you will need to treat the amended petition as your first petition. This would include re-publishing the Petition with a newspaper and serving all required parties. See Local Rule 4.27 and CRC 7.53 (links provided below).
Another option would be to supplement the pleading and serve on all required parties. Generally, a supplement would respond to any issues identified by the Probate Attorney on the probate notes before a hearing; however, you may be able to supplement the Petition with the corrections you described in your question. Without being uncertain where the mistake lies, I cannot recommend which is the better option for you.
Finally, if there is no will, then you will are petitioning to be the "Administrator" of the Estate; an executor applies when there is a will.
I truly hope the information and links provided an answer to your question.
You can file an amended petition and list yourself as both the petitioner and also as the person being nominated to administer the estate ... assuming that the hearing date has not already occurred.
You indicate that you want to be the "sole executor/administrator" and also the "trustee". If your mother had a trust, then only the person named in that document as the "successor trustee" can be the trustee. If your mother didn't have a trust, the probate court will not create one now.
Although there are many reasons for wanting to be the executor/administrator/trustee of a person's estate, I suspect that one of your reasons might be that you think if you're in charge, you can do what you please and not have to distribute anything to your siblings. That's not going to fly....
It also seems to me like you're trying to do this yourself. As you can already see, it's not quite as easy as one might think. I urge you to get a competent probate lawyer to assist you.
The response given is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change. Attorney is licensed to practice law only in the State of California. Responses are based solely on California law unless stated otherwise.
As the other attorney's have stated you can file an Amended petition correcting the mistake as long as the hearing has not taken place. You should also become familiar with what probate is and how it works or it will be a long, difficult process of mistakes and amendments. Probate is not simple. If your mother had a will and/or trust you may be wasting your time unless you were named executor and/or trustee. If she had neither, you would be petitioning as administrator of her estate (not executor). Hopefully you have published and served Notice and have your other documents in order for the hearing as well. Your notice needs to reflect the correct person you want named as administrator so if you already did that with your sister's name on it you will have to start publication over as well. Since your mother left a big estate, you really want to consider using some of the estate money to pay a lawyer. You do not have to pay for it yourself, it comes from the estate, and it would be money well spent.