Hi Mary and welcome to the Forum.
I can relate to what you say about wanting chicks for your children, as back in the 70s I got worn down at last by my eldest crying herself to sleep at night for weeks because she wanted some. We ended up with 8 Silkie chicks, a week old, at which she you can't sex them. 6 were cockerels ......
Like you, I tend to want everything done yesterday, but when you're thinking of taking on livestock of any kind, it's good to consider what's going to happen in the next few years. Chicks are sweet and fluffy for about 6 weeks, after which they get big very fast and need a secure outdoor run and coop, which need to be ready in advance, quite considerable outlay for the quality which will last for at least their lifespan of up to 6-8 years,(in addition to the cost of an incubator and brooding equipment) The reason people don't usually hatch at thus time of year is that chicks also need sunshine to develop properly, unless reared in a hatchery with lots of special 'daylight' light. Whilst they can be kept in a brooder box indoors for a few weeks, they take up a lot of room as they grow, and are very messy and produce a lot of feather dust, not good in confined spaces. It can be done, have a look in our hatching and rearing section to find out what it entails though. Also, you need fertile eggs from a proper breeder, and at this time of year most non-commercial hens are not laying, again because of lack of light which causes hormonal changes. Any eggs produced by a mixed flock running with a cockerel are probably not very fertile either, until the Spring breeding season arrives. Very few laying hens nowadays ever even see a cockerel, relatively few people keep them, and all the eggs you buy in winter from egg farms will be from flocks of single-sex hens living under extra electric light to keep them in lay, so the eggs are 100% non-fertile.
Integrating any surplus 'spares' with a larger flock would also be far from trouble free, as chickens are always very resentful of newcomers and young birds would be mercilessly bullied. Also, the school would probably not welcome cockerels. Like any pets, chickens aren't toys, they're a long term commitment, and their care devolves upon the adults once they've grown up and are no longer fluffy and the kids have got tired of their new 'toys'!