Most families handle an aging parent with a set of verbal promises. Your brother will take the holidays. Your sister will cover the doctor visits if she is in town. You will do the afternoons because you live closest. Everyone nods, and for a while it works. Then someone's job changes, a kid needs more time, or a bill arrives that nobody expected, and the promises turn out to be different in each person's memory. A short written agreement is not a legal contract. It is a shared record of what you all said you would do.
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What belongs on the page
Start with the things that cause the most friction. Write down which days and times each person covers, what happens when someone cannot make their time, and who decides when a change is needed. Add a line for money: which costs are shared, how they are split, and who keeps the receipts. Include a line for decisions that are not about money or time, such as who talks to the doctor's office or who gets the first call when something goes wrong. Keep each item short enough that a tired person can read it in one minute.
What to ask before you sign anything
Ask how often the agreement will be reviewed and what triggers a review. Ask what happens if someone wants out. Ask who has the final copy and where it lives, so it is not buried in one person's email. If money is involved, ask whether a bank account, a shared spreadsheet, or a simple written note would make the record clearer for everyone. If you are unsure whether a document needs more formal steps, a lawyer or a bank representative can tell you what your situation calls for. This article does not give legal advice.
Compare the time you are asking for
Look at the real hours each person can give, not the hours they wish they could give. If your part of the agreement is the afternoons, check how many of them still fit your work schedule and your kids' pickup. If your sibling's part is the weekends, check whether they are actually around on the weekends that matter. An agreement that cannot survive a normal week will break the first time something unusual happens.
Revisit it on a schedule
Choose a date each year, or a set of triggers such as a move, a new job, or a change in your mom's needs, to look at the agreement together again. This is not a sign that someone is failing. It is the way a shared plan keeps working as life changes around it.