I just signed on and saw your question has not been answered. I hope this response is still helpful. The following site goes over heimlich for dogs.http://www.petplace.com/dogs/heimlich-for-your-dog/page1.aspx
If your dog is panting there are many different things can cause constant panting. Heavy panting can be caused by heart problems, lung problems, fever, or bronchitis. You can read about this here:http://www.petplace.com/dogs/panting-in-dogs/page1.aspx
Dogs pant for various reasons. They pant to cool down, but they also pant when they are under stress, in pain, or afraid. There can also be medical causes such as neurological problems, respiratory disorders, and Heart problems such as heartworm, anemia, and fever.
If your dog is indeed having difficulties breathing, she should be taken to the vet immediately. Allergic responses can cause swelling of the throat and need to be addressed prompltly. If this is the case, Benadryl can be given to your dog, the dose is up to 2mg per pound every 8 hours. You can read about these here. http://www.sniksnak.com/doghealth/inhalants.html
If you think this might be a severe cough, there are things you can do to help. To help your dog breathe easier you can run a NON-medicated humidifier in the room your dog is in, or sit in a steamed up bathroom with your dog to help keep the mucous moving. Robitussin DM at a 1/4 teaspoon per 5 pounds can be used to control the cough. Dosages can be obtained at this website. http://www.petplace.com/drug-library/dextromethorphan-robitussin-dm/page1.aspx
Again, if your dog is having difficulties breathing she should be seen by your vet immediately. Hope this helps.
Unfortunately, insulation would definitely cause throat irritation and coughing. This can be very dangerous to your dogs. If you think your dogs really ingested it, you should take your dogs to the Vet. Many types of insulation are like spun glass. These shards can be embedded in your dog's throat, stomach and gastrointestinal tract. This could cause internal bleeding. If you elect to wait, then if your dog starts vomiting or having diarrhea, I'd take them in immediately. Keep an eye on their gums and if they become pale, that would signal possible internal bleeding and they would need to be seen. I'd go ahead and give each dog a spoonful or two of canned pumpkin (not pie filling) on some food. Hopefully, if there has been some ingested, the pumpkin will pick it up and allow it to pass through their systems. I would call my Vet as well to let him know just in case you end up having to take them in.
While some molds can cause respiration issues, the insulation would definitely irritate the throat. Knowing dogs, it is very possible they were playing tug of war with it since you found it all over the back yard. Definitely try the pumpkin and monitor all the dogs closely if you decide not to have them seen.I hope this information is helpful to you.