In the early fall, I have an influx of what is referred to around here as ground hornets. They are about the size of a honey bee, but are definitely in the hornet or wasp family. They are black with pale yellow stripes and we can observe them carrying dead insects to their entrance and into what's obviously their nest. My dilemma is that we have had a nest of them in the siding on our house. I got rid of about a quarter of the population by rigging a Shopvac to the side of the house, treating a rag with hornet killer and vacuuming them into the Shopvac and killing them, but I know I didn't get them all. Also, I removed a trim board to expose the area to the cold, during which time the temperature got down into the low teens for an extended time, hoping this would kill the remainder. If they survived my onslaught, is there a balm or penetrating spray I can use?

Spraying into the entrance with a Clear Zone Pyrethrum Aerosol or PT Wasp and Hornet Spray should do the job.

Use a pyrethrum aerosol with a crack and crevice straw or the wasp and hornet spray.. Inject the spray into the openings at night

Note: It's very important to do at night because they are all in the nest and much less likely to attack you.
They don't see well in low light.
This should take care of the problem.

We have these insects that we cannot identify : winged, black in color. They are flying insects that are burrowing perfectly round (about 1cm in diameter) in the ground with the dry dirt around it along the border of the lawn closest to the house and through the cracks in the sidewalk. They disappear at night. Are they carpenter bees ?

These are commonly called Digger Wasp. Spread Talstar Granulars or Bifen LP over the area.