Hurrah! and phew!
Somewhat at the eleventh hour and rather to my amazement, we did in fact manage to get the buggy axle back together.
Even putting on the new and rather large G clamp didn't quite do it, but then with human force applied to the "free end" of the G clamp in exactly the right direction, it sort of rotated enough into place that I could get the bolt back in.
It was the "eleventh hour" inasmuch as I had started thinking it was impossible without either a friendly weightlifter person or special equipment, and had started thinking about getting in touch with the manufacturers or with this muscly person I remember from the gym who seems friendly. And I was speculating on how much the courier would cost to send it somewhere and how much the repair might be and telling myself "ah well, it's only money". I really didn't think we were going to do it and I was thinking somewhat ruefully of my predicted "80% chance" from yesterday.
But somehow even after having those thoughts, I couldn't resist poking and prodding the axle around a bit more. I took it apart again and put it together without the spring and drew pencil lines on one bit to show where the other bit ought to line up. And then when applying the force, we were able to aim for the pencil lines, which helped. Right up till the moment when the bolt actually went into position, I wasn't really expecting it to work, and I'm still rather astonished that it did!
and I've been feeling very lucky and successful all the rest of the day. Which is funny in a way considering that the whole episode only got me back to where I was before I made the mistake. (As it said in a book I read the other day, happiness of the moment is very much based on things turning out better than you expected - relative, rather than absolute.)
Separate from that, I've also managed to improve the behaviour of the brake, by adjusting a sort of tension adjuster thing on it and possibly also assisted by lubricating some key places. (It's not a friction brake, so no worry about lubricant getting out of hand - it works by a small metal post slotting into a coggy bit.) It still has a "pretending to be on when it isn't" setting, which i.m.o. is quite a serious design flaw in a buggy brake, but my tweakings have reduced the frequency of that back down to a reasonable level.
So, on the whole, hurrah! and thanks to all who offered encouragement, luck etc.