In a full house, the bathroom is not a room. It is a clock with several people waiting on it. Most of the morning friction does not come from anyone being unreasonable. It comes from nobody having counted the minutes. Count them, and the fight becomes an arithmetic problem you can solve.
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Write down the fixed times first
Start with what cannot move: the school bus, the first shift, the carpool, the time your parent's breakfast or medication routine is anchored to. Write each fixed time on a sheet with the bathroom time beside it. The fixed times are the walls of the schedule. Everything else has to fit between them.
Time each person's routine honestly
Use a phone timer for one normal week and record how long each person actually spends in the bathroom, including the slow parts: the hair, the brushing, the help getting dressed, the transfer onto the toilet or into the shower. Most people guess low. Your parent's routine will almost always take longer than the family estimate, so measure it rather than assuming.
Find the overlap
Lay the times side by side. Mark every window where two people need the bathroom in the same ten minutes. Those windows are where the plan breaks. Your options are to move one routine earlier or later, to split the routine so part of it happens in the bedroom, or to create a second place for the simpler tasks, such as a basin and wipes for washing up, which removes one full trip from the crowded hour.
Decide who keeps the door
Someone has to say whose turn it is when two people are standing outside. Name that person in writing. If the answer is you, count that as a daily job, and add the minutes to your own total. If the answer is the children, make sure they know what the job involves and that it is not a punishment.
Check the room for the routine you have now
Look at the bathroom as it works today, not as it worked before your parent moved in. Is there a place to sit that is not the edge of the tub? Is there a grab point within reach of the toilet? Is the floor non-slip when wet? Those are not decorating questions. They decide how long each routine takes and whether anyone gets hurt during the rush.
Test the schedule for a week
Run the new plan for seven mornings and keep a short note each day: what was late, what was rushed, who was waiting. Adjust once, then keep the version that held. A schedule that has been tested for a week is more useful than one that looks perfect on paper.
If the mornings still do not fit after a month of adjustments, the problem is usually the number of people sharing one room, not the plan. That is information you can use when you decide what to change next.