When the ride is a family, not a passenger
Four people and two car seats is not a taxi ride with extra people in it. It is a different vehicle and a different calculation.
The counts come first
Adults, children, and the ages that require a seat, plus the suitcase and buggy count. Those numbers decide the car before anything else is discussed, and they are the first thing asked when you book.
Child seats
Say what you need and the arrangement is confirmed in the booking thread. What will not happen is a promise that a seat is in the boot when nobody checked.
Early flights with children
The pre-dawn departure is harder with a family, which is exactly why it is booked rather than attempted. Address, hour, cases, buggy, seats — and the morning becomes a timetable instead of a gamble.
Questions
Can you take a folded buggy and three cases?
Say the numbers when you book. A larger vehicle can be arranged subject to availability.
Do you provide child seats?
Ask when you book and the answer is confirmed. It is never assumed.