Nobody in the group text argues about the smoke alarm until it starts chirping in the middle of the night. That chirp is the whole problem in one sound: a low-battery warning that somebody heard once, assumed someone else would handle, and then forgot. Your mother's alarms are a small job, but small jobs like this tend to land on the one daughter who lives closest. Settle it before the chirp settles it for you.
Count what is actually in the house
Walk the house with a notepad before anyone buys anything. Write down every smoke alarm and every carbon monoxide alarm, room by room, including the hallway unit, any unit near the furnace or water heater, and any in a garage or basement. Note whether each one runs on batteries only, plugs in with a battery backup, or is hardwired into the house wiring. Some alarms are linked so that one going off sounds all of them. Note that too, because linked units are usually replaced as a set, not one at a time.
Then check the back or side of each unit for the manufacturer's date and replacement guidance. Alarms do not last forever, and the sensor can wear out even when the battery is fine. Write the replacement year on your list next to each unit. That is the line item most families miss, because a working alarm gives no sign that it is old.
Assign three jobs, not one
Most of the friction hides inside the word alarms. Split it into three jobs and give each one a name.
The monthly test. One person presses the test button on each unit once a month and marks it on the calendar on the refrigerator. Pick an easy day, like the first Sunday, and write down whose day it is. If your mother can still press a button and hear the sound, she can do this part with a reminder. If she cannot, the test belongs to whoever visits most often.
The battery change. Decide who buys the batteries, who installs them, and how often the change happens. Many families change batteries once a year on a set day, which is easier to keep than waiting for the chirp. Decide, too, who your mother should call if a chirp starts and nobody is nearby.
The replacement. This is the job that costs real money and gets postponed longest. Decide who orders replacement units when the printed date comes up, who pays, and who installs them. Put it in writing. If the cost is split, say exactly how, and say whether it comes from your mother's money or the family's.
Check the questions before you buy
Before anyone orders a unit, confirm a few things you can verify yourself. Check whether each unit is a smoke alarm, a carbon monoxide alarm, or a combination, because they are not interchangeable. Check whether the replacement has to match an existing linked or hardwired system. Ask the seller to show you the packaging so you know whether you are buying a sealed long-life battery model or a standard battery model before you pay. Ask your local fire protection district whether it offers alarm checks or installation help for residents, and whether there is a fee. The local help page is a good place to start, and the sources page lists the public pages this guide relies on.
If someone offers to install hardwired units, ask whether that person is licensed or insured for the electrical work where it applies. Hardwired alarms are not a weekend project for everyone, and an install that looks finished but was done wrong is the kind of thing you want to catch while it is still easy to fix.
Write the handoff
Put the whole plan on one page: each alarm's location, type, replacement year, test day, battery owner, and replacement owner. Keep a copy in your mother's kitchen and another in your own files. The next time someone asks who handles the alarms, the answer is on paper, and nobody has to rebuild the arrangement from memory in a group text.