Doesn't need to be kids - I have had a double puncture before, probably on my way from work and not known about it till the next day when both were flat. (tried turning them until the flat bit was at the top but it was no use)

I remembered this one from my old army winter warfare exercises donkeys ago!
Try taking the wheels off the car and getting them warmed through in the house, or fill the bath with hot water to almost tyre rim height and rotate it till the tyre is warm then try to inflate it. Don't forget to rub some washing up liquid around the tyre bead to lubricate it first.
or
Try to get one of your m8s to take them to a garage for you, inflate them and bring them back to you might be worth a try.
or
The RAC/AA/GreenFlag recovery service?

Found out myself that those electric tyre inflaters are more a gimmick than useful most of the time. Even the old double barrelled foot pump was more efficient.
The best method would be to remove the tyre valve and inflate until it reseated on the rim but I doubt if the electric inflater has the guts to do it.
GudLuk