I am so sorry. Nothing I could say would make you feel better, but I really am sorry. It is so hard to lose a parent.
I want to tell you that you need to go to her doctor now and get a DNR for her that is signed by the doctor. Tell them you want it for her at home.
The laws of your state may be different from mine, but when my sister died at home, my mother called the paramedics and they came. She was on her last breaths, and they were there with her, along with my mother. The DNR was displayed on the wall for the medics to see. They took my sister directly to the funeral home.
The point I am making is that you need to talk to the doctor and find out exactly what to do. Find out what the law says for your state. Have the coroner's phone number. Be ready.
I will tell you after having lost 2 family members (including this sister) to conditions that not having a DNR would have been cruel and unhelpful, that even having one is SO hard, because in the stark realization of the end of that precious life in front of you, it's so hard to tell the medics not to do anything, but instead to honor the DNR. Sometimes, the only way you can bear to do what is best for your loved one and do what they want, is to have that DNR in front of you. And it also saves you from some legal responsibilities with interfering family members who are not supposed to have a say, but want one anyway. (I would hate to call them drama queens/kings, but some of them act like that, trying to swoop in and take control because they have not been part of the process, but all of a sudden realize they haven't been in the patient's life enough, and now want to change that.)
Make sure there is a signed will. Make sure it's not in a bank security box. The bank will not open it after she dies without legal documents, and you need that will in order to start the process. If you think that family members will argue about a will that is recently signed, video her. An estate attorney can help with this. Life insurance? Where are the papers? You need to find that - with all the papers, the funeral home will take care of all of that for you all. It's a blessing, really. They will get the death certificate ordered for you (you will have to pay for that), and as soon as they receive them, they can get the life insurance work started.
Where is the title to the car? House? Do you have bank account statements? You will need to take the death certificate down to the court house along with her will, and a blue book value sheet that shows how much the car is worth. Call for an appointment (you aren't supposed to just show up) and the court officer will give you Letters of Testamentary. You will need to take these to the bank and open up an estate bank account. Make sure that you don't pay ANY of her bills from your own bank account. You can't get your money back if you write a check from your own account. You have to write it from the estate account.
Please, please, please, go ahead and write her obituary. She can talk to you about what she wants it to say. Do not put her birthdate in the obituary. Do not put her address in the obituary either. People have been robbed during the funeral because it was known that the family wouldn't be at home at that time. If you have family members who would like to help, that is very special. We did that for my mother-in-law. It was so much better than having to write my dad's in the middle of the night after I had just flown in from overseas. My mom couldn't do it and I had to do it for her. It has to be done for legal purposes quickly. You will want to email it to the funeral home (digital copy so that no misspellings retyping it will happen.) If you have already met with the funeral home, which I think you have, they will have a file on your mother and they will put the picture in her file and have the email ready to send to the paper after adding the date of death. They will send it for you to the newspapers you want them to go to. Ask the funeral home how much the specific papers charge per line and for a photograph to be added.
Sometimes a funeral home will ask for a form to be filled out when you come to them. Have they done this for your mom? For cremation, there is usually something to sign in advance. Talk to them about this.
Even with the cremation, you will want to choose something for your mom to wear. It's easier to do that now than to wait.
As soon as you have received the death certificates, look up the addresses of all 3 credit reporting agencies and write them a letter telling them about your mother passing. Include her social security number in the letter and ask them to freeze her account and mark it as deceased so that no one can open fraudulent credit in her name. You have to send a COPY (not an original - I found that out the hard way when they sent the original back and I had to start over) along with the letter.
You will need to call the credit card companies, her car insurance company if she still drives, and you will need to go down to the social security office. I would call the social security office and find out what all documents you will need to bring. Take a snack and a book because you'll wait for a long time in the social security office...
This is just a small amount of what has to be done, but it's the first part of what has to be done, and will get you started.
I know that none of this talks about how to grieve or how not to have people at the funeral, but your questions reminded me of these things that I had to help my mother with. Sometimes knowing these kinds of things in advance so that you can get them done can help a little with your grief. Some people need to DO something. Some people are paralyzed and can't do anything. And some people step up and do because somebody HAS to.