What's so hard about taking the donut-wheel down to a gas station to inflate?
Or for that matter, use the second car to deliver the standard wheel/tire to/from the repair shop (Costco?) and mount it in your own driveway.
Then either 1) take the donut-spare to a shop to look at or 2) get another one from a wrecking yard.

It's not clear yet in this thread what condition the donut-spare is in. Has the bead separated from the rim?
Is it only deflated?

Don't want to put the tire on yourself?
Got Tripple-A?

Hope you find a solution-