I don't like the illustration on the cover of this edition. The edition I read made it clear that the story takes place, not in the 1950s, but in the 1920s, and are the same as the internal illustrations in this book. Furthermore, the language is anything but 'old-fashioned'. People tend to forget that the 1920s were a revolutionary era, and that the modernization they began was shunted onto a siding by the Depression, the War, and the subsequent marterialistic conservatism--and only began to emerge from its cocoon in the late 50s.
The first time I read this book I did notice that there was a moralistic rejection of pacifism, and that's continued to jar me at every rereading. War games for children are defended as 'ordinary and fun', and the quite rightful rejection of them by Jane's foster family is ridiculed. These fantasies of romantically idealized violence were explicitly and deliberately designed to teach children to be killers, and, (as James While pointed out in Final Diagnosis), were designed to depersonalize the 'enemies' that were invented to justify the violence. Continuing to espouse the training programs for imperialism isn't appropriate now--and it wasn't appropriate then. The foster family are stick-in the mud types, granted. But the problem is that too many fantasy writers of the period argued that it's only POSSIBLE to hold these anti-militarist views if you're priggish and stuck up.
It should be noted that the landscapes the children are transported to, for all their realistic detail, are not intended to represent real places. This may not be so obvious in the Arabian Nights-esque desert (which would, by the way, be the Rub-al-Khali, not the Sahara), but it should become obvious when the children are 'returned' to a nonexistent past, ie Camelot.
The adults, being more conditioned to be sensible, tend to go to real places, even by magic. And the children do have some adventures in the 'real' world. But the farfaring parts are wholly imaginary--or perhaps 'legendary' is a better term.
I never had any problem with the mother wanting to leave her job. It wasn't a good job, clearly. I don't even object to her wanting to be a stay-at-home mom--provided it's clearly stipulated that a man in the same situation could want (and achieve) the same thing. I don't think much, however, of the notion that this can only be achieved by magical means. The social assumptions in this book (and other books by the same author) are often disturbing. I wouldn't care to live in a world run according to Eager's morality.
I do agree that the children are believable and (as much as fallible mortals can be) good, responsible people. And I wouldn't probably have minded playing with them as a child. I just resent being told that abusive behavior is normative.
A lot of the language that's stigmatized as old-fashioned comes out of the children's dedication to gay '90s (meaning the 1890s) children's literature (specifically and explicitly E Nesbit, but also including things like Evangeline, which was from earlier yet). If you're not familiar with the originals, you'll often mistake quotations for original dialog. Before E Nesbit, very little literature for children included the children's fantasy lives, which color and influence even (or perhaps especially) magical adventures. The children are not living in just one dimension of time at any point--but especially not when they are influenced by magic.
The move to integrate adult's fantasy lives into stories about them mostly came later--about the time this book was written, I'd say, generally. But since Half-Magic was SET in the 1920s, there's little attempt to do this, and it's mostly ridiculed when it is shown. Other books, unfortunately, tend to incorporate almost solely sexual fantasies, which are too often musky and insubstantial, at least partly because the majority of adult fantasies may incorporate sex, but aren't predominantly about sex. Eager doesn't even try. He tends to either completely excise the fantasies of the adults, or to marginalize them, or to meake them seem pedestrian, as if to imply that puberty completely shuts off the capacity for fantasy. This has the result of making the adults somewhat shadowless and insubstantial.