2 kids one car. The kids walk to school, one of us works at home and the other takes bus and luas across Dublin to work (public transport is faster and cheaper in our case). The car is mostly used for food shopping, bringing kids to sports activities all over the Dublin area, and for weekend visits to the country.
Is the car essential? Well the trips to the country would be more difficult and we'd never be able to do anything when we're there without relying on others... In Dublin, less essential. We live close to city centre and often walk into town (and home again). We are well served by public transport.
I agree that the use of cars to ferry kids to school is a problem, and a very significant contributor to road congestion, as can be seen in most areas when the roads suddenly become much more manageable during school breaks. People use all kinds of reasons to justify this: no public transport, too dangerous to walk/cycle etc. Part of the problem also is parents insisting on sending their kids to private schools far from home rather than use the supposedly inferior public school nearby. And part of it is snobbery. I know several people who think that buses are only for immigrants. Another friend has returned to the country and is getting grief from family members for planning to buy a used rather than a new car ("the shame of it, the neighbours seeing them driving up with their 98 reg plates" etc etc).
The more we use cars, the less efficient public transport becomes. It's a self fulfilling prophecy. Many people insist that the public transport system is "not available" where they live, but I am always suspicious of such claims from people who live in Dublin. Sure, there is room for improvement in public transport, but we have to demonstrate a willingness - an insistence even - on using it. Incentives could and should be provided for this. Many companies operate the revenue approved scheme whereby your buy a bus/train/luas pass from pre-tax income, but not everyone knows about this.
Many others, unfortunately, don't care.