Eating feces is called Coprophagia. Many dogs eat their own feces. Some eat any feces they find. No cause has been determined as to why dogs do this though some believe it may be a dietary deficiency while others believe it to be an obsessive compulsion disorder. In your dog's case it is likely the result of her having a litter or multiple litters of pups. Mothers of pups ingest fecal matter and urine to keep the whelping area clean. Usually it is the pups fecal matter, but if she was a puppy mill pup, she may have had to ingest her own as well to keep her pups in a cleaner area.
If you are not feeding your dog a high quality dog food, you may wish to try switching foods. Some believe that if a dog is experiencing mal absorption problems the stool will smell like food and thus the dog eats it thinking it is food. As parasites are contracted frequently through feces, your dog should be tested for parasites. Blood tests can be run to rule out a medical cause. The best thing to do is try and curb your dog's tendency to do it. You are already doing one the most important things we recommend to stop the behavior by removing feces out of the yard as soon as possible and keep it cleaned up. You can also put hot sauce or other pepper product on them so the dog finds then terrible tasting. There are over the counter products that you can give your dog daily to prevent this condition. They work in some cases and if it works for you, then it’s an easy solution. You can buy them at most pet stores. One is called forbid, but they do have lots of them. Most are similar. Basically they make the fecal matter taste really bad, so the dog stops ingesting it.
It will be harder to treat if your dog eats it’s own feces right after going. You will need to be with your dog when it is going and divert your dog away from it, praising your dog when she does not try and eat it. A firm “leave it” and correction should be said when she tries to eat it and comes in handy in the future for other items you do not want your dog eating.
You can read more about Coprophagia here.
Some experts believe a raw food diet helps stop the problem. One thing with a raw food diet is that there is less filler in raw food diet and thus less fecal matter and it would smell less like food as all of it would be waste product and not undigestable fillers. So it may be worth considering. I have heard of some trainers suggesting a cone on the dog when letting them out to eliminate. The cone prevents them from being able to eat the fecal matter. Some people even resort to electronic training collars to stop the behavior. Since you would be at a distance, the dog would not associate the correction with you but would associate it with the fecal matter. I usually only recommend training collars for long distance recalls, but I did want to give you the various techniques that other people have used with some success.
For the trash cans, there are a couple of things that are effective. One would be to put your girl on a leash and put a trash can with some tasty things inside in the middle of the room. You will also need a lot of hot dog slivers to use as treats. If she goes toward the trash can, give her a short tug to get her attention on you and then a firm low toned NO so she understands you do not want her to go toward the trash can. It may take a few times but she will soon not even try to get to the trash can. When that happens you will reward the behavior with a tasty hot dog sliver. You want her to realize that it is more advantageous for her to NOT get in the trash can then to disturb the trash. You will practice first in the family room/living room and once she has the general idea you will move to the actual rooms where the cans are stored normally and repeat the training. It is going to take a lot of work but it can deter a dog from going into the trash cans.
You may want to get timed feeder or treat dispenser that will release a treat every once in a while. This may probide her enough stimulation to keep her occupied and out of the trash. Another thing that I have found works great is getting the wooden trash cans with lids and putting portable entry alarms on them. You need the ones you can disable so when you want to use them they don't go off, but if she goes to get into the trash by lifting the lid, the alarm will sound and provide negative reinforcement which stops the behavior. See one here:
Many of my clients have elected this solution and have been very please with how fast this solution worked to keep their dogs out of the trash.
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Since there have been recalls on certain foods, please check the following site to be sure the food your animals eat is not affected. If it is affected, contact your vet as soon as possible. Have your dog seen if they have any symptoms.