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Two lessons, one car: the part generic software gets wrong
Appointment software gives every resource its own calendar, and that works when the thing being booked is a haircut. A driving lesson consumes two things at once, and the moment one is taken, the other has to go with it.
Here is the shape of the problem. You have three instructors and two cars. Marcus drives the Corolla, Priya drives the Elantra, and on Saturdays Tom takes whichever is free. Book Marcus at 10am and you have booked the Corolla at 10am, whether or not anybody wrote that down.
Now put it in a system that books appointments. You create three calendars, one per instructor, and it works — until the Corolla goes in for service. Marcus is still bookable. The software has no idea he cannot teach without a car, because it was never told that a lesson is two things.
Capacity is not one number
Ask a school how many lessons they can run at 4pm on a Wednesday and you get a pause, because the honest answer is a minimum of three separate numbers: how many instructors are working, how many cars are on the road, and how many of those instructors are allowed in that car.
The smallest of the three is the answer. Three instructors and two cars is two lessons, not three. Two instructors and four cars is still two. Software that counts one pool will get this right roughly half the time, which is worse than getting it wrong consistently, because you stop checking.
The turnaround is real time
A lesson that ends at 11am does not free the car at 11am. The instructor has to get back, and if the next student is across town, that is twenty minutes nobody put in the calendar. Schools handle this by leaving mental gaps, which works until the person with the mental model takes a week off.
The fix is not discipline. It is putting the gap in the same place as the booking, so it applies whether or not anyone remembers.
Working hours are not opening hours
This is the one that quietly costs bookings. Your school is open nine to eight. Priya works nine to three, Tom works three to eight, and on Saturday only Tom is in, eight to two.
A site that advertises “9am–8pm” on every day is making a promise it cannot keep on Saturday afternoon. The parent picks four o'clock, gets told no, and reads that as a broken website rather than a staffing fact. The hours a school is open and the hours it can actually teach are two different things, and only one of them belongs on the booking page.
One question sorts it
“If the Corolla goes in for service on Thursday, does Marcus stop being offered on Thursday?”
If the answer involves you blocking a calendar by hand, the answer is no. And the day you forget is the day a student is standing outside their house at 10am with nobody coming.
What this means for your website
You tell us what you have — three instructors, two cars, who drives what — and when each of them works. A booking takes both at once, the turnaround is held automatically, and the hours offered come from who is actually on that day.
An instructor who always drives the same car can be locked to it, so when that car is off the road the instructor is not offered either.