Pre-planning. Any advice?

If hospice isn't involved, you would call 911. Someone needs to pronounce the death. Have mom put her burial wishes in writing. The funeral home will pick up her body. They file for the death certificate I believe. My dad wanted to be cremated and 'swim' with the Dolphins so his ashes were placed in a biodegradable turtle & released in the ocean. We kept some of his ashes

Now would be the time to plan funeral if there will be one.
And prepaying is a good plan as well.
You would tell the funeral home exactly what you wanted done and they will arrange what needs to be done.
If mom is on Hospice all you have to do is call Hospice and they will take care of everything.
I urge you to contact Hospice. Call the one of your choice, interview a couple if you want. You will get support from a wonderful team of people. A Nurse that will come at least 1 time a week, more often if needed, a CNA will come 2 to 3 times a week to give a bath or shower and order supplies. You will get all the supplies briefs (aka diapers) pads, gloves, ointments delivered as well as equipment and medications delivered. You can request a Volunteer that will come and sit with mom while you get out and get things done for yourself. AND big bonus if you need a break you can get Respite, almost a week is covered/paid for by Medicare.
If she is not on Hospice then you would call 911.

My mother died in the night at home, totally expected. I phoned the GP the next morning at a reasonable hour, and he came and wrote the death certificate. I phoned around for simple funerals, chose one, and they collected her body later in the day. No dramas.

You can plan ahead for costs at any funeral home or crematory. You will discuss costs. For peace of mind when thinking straight at the time of death may be tough, you can do it early. For the tombstone, if you need to have them put date of death, some stones have a little marker on them with the business name. Sometimes you can find the info at the cemetery. There will be costs associated with burial.
If she passes, you need to call non emergency police,but if witnessed and you want to start CPR, then it is 911. Even if you do call for CPR, chances are low on survival. The coronor will need to come by and pronounce. If you can get her on hospice, then you have more support. With hospice, you call their number then they will send out their APRN to pronounce. Both ways, you will need her Social Security number for death certificate paperwork if you have it. After paperwork is done then you can call the funeral home, unless death is suspicious. Expect the body to remain at the location for a couple of hours.

When my husband died at home from ALS at 54 years old 911 was called and they sent the police and an ambulance. We told 911 that he passed but in our state when someone dies at home the police must come and rule it a natural death. They checked the scene, questioned the family, and then a coroner was called. His wishes were to be cremated so I signed the paperwork with the coroner and his body was taken away. The laws of the state will dictate who is called but you can start with his PCP or 911.

Yes, have a place picked out for them to take her. Unless you plan to have a service at that location, don't go with a mortuary but rather with a place that just does cremations.

I learned that the hard way. My dad died first, so I used the mortuary everyone used in town. His cremation was $2800 including a dozen death certificates they talked me into buying.

When Mom died last year, I used a cremation-only place, and bought only five certificates (also too many). Total cost: about $800.

I've never needed more than one death certificate, as everyone who asks for one makes a copy and hands it back to me. The only one I haven't gotten back was the one the escrow company wanted when I sold their house, but apparently that one will also be returned.

Don’t call 911. Call her Dr. who will take care of the death certificate and then call the local funeral facility. It might help to call the original plan to see if they work with a local company.

Some of this depends on your state and local laws. Most localities if the person is NOT on at home hospice (which a physician would have had to order and therefore 'impending death" is expected even if that over a long period of time AND then hospice would be called when death occurred) want the local police called in to assure there was no "suspected wrong doing" a death that occurred at home.

If hospice is indeed involved already, they would have worked out with you the next steps when death occurs: call them, they would have set up the who picks up the body, where is goes etc. all as part of the their planning. And yes, best to think all this through and made what decisions you can now so when the time comes it is not just more to deal with. One can also pre pay funeral costs so that part is all done too.

If hospice is not involved and death occurs at home, most likely the local police must be involved (again to rule out any possible wrong doing in the death). This happened with an elderly aunt. She passed unexpectedly in the night -- likely heart attack, in bed -- her brother (my uncle) found her in the am. They (bother and sister) lived in the same home. He call me and I said you have to call the local police, call the non-emergency line rather than 911. The police arrived, just before I got there w/my mom at the time. My cousin also arrived. ALL who showed up even if NOT there when the death occurred had to be interviewed by the police so one thing (I did not know) is do not have more and more people show up at the house and that means hours and hours more of the police interviewing all there.

It took about 3 hours for those interviews, each done individually and separated from the others all while the body layer in the bed (awful). Finally, the interviewing was done, the local coroner person showed to write the death certificate and THEN we were given permission to call a funeral home to pick up the body. They cam 2 hours later. So start to finish, this was a full day. Again, if I had known, I would have advised my Uncle to call non-emergency and to NOT ask anyone else to come over as that just slowed the entire process down to a snails pace.

If you can get the DNR in place and hospice, this will be so much easier when the time actually come.

Sorry you are having to deal with this, none of this is explained or written in a how two book but there is lots of good advice here on this site. Talk w/your mom's physician about getting that DNR in place if not existing now and about ordering hospice. And ask the physician what he/she advises at the time of death if hospice is not yet on deck.

If she is not on Hospice at home, you call 911. If on Hospice you call the Hospice nurse. You tell them what funeral home you want the body taken.

We just went through this with mom.

She died at home, nobody else was there. YB simply called the mortuary and they scheduled a time to come get her body. She was not on Hospice, but aged 92 and we knew she didn't have a lot longer. The police were not called either.

Maybe it varies from state to state.