What do you do when a dog is choking? Our family lives in the country and the Vet is unable to pay us a visit.

Prince, they have found the heimlich maneuver works for dogs as well as people.
Since you are unable to get immediate help, it may be wise to take a first aid course for pets. The American Red Cross offers these courses. I am including a number of links that should help you.

First Aid for Dog Choking. Help for a choking dog

Causes of Dog Trauma

Pet Tales: Learn how to help a choking dog

Pet First Aid Class Offers Peace of Mind

Was this just a general question or have you lost your dog in this way? If you have, I am so sorry. I know how upsetting and devastating it can be when we see our pets suffering and there is nothing we can do to help.

I am sure this it too late to help you, but I would like to help others avoid the same thing.

The pet stores are full of toys that many dogs will quickly chew up into
Pieces they could choke on or cause intestinal blockages. If you are not
There to watch, stick to sturdy stuff such as Nylabones and Kongs. Keep a
Close eye on chew toys and quickly discard anything that is coming apart in
Pieces. Rawhide is especially bad because it swells after being swallowed.
These problems are the worst with, but not limited to, large, aggressive
Chewers such as Labs.

Ropes from the pets' store quickly turn to hazardous shreds. Ones I made
Lasted much better. Go to a hardware or home center that sells rope by the
Foot. Buy 2' of 3/4" poly rope. Melt the ends, and tie knots in it. Get
Them as tight as possible, put it in a vise and pound it with a hammer. Watch
Carefully, and be ready to discard when it comes apart.