Enlarged prostates in dogs is common among intact males. It can be caused by several things.
1. Benign Prostatic Hyperplasia (BPH): Which is a natural swelling of the prostate as the dog ages. Most common.
2. Bacterial Infection: Originating from the blood stream or the urinary tract. Infections can be acute or chronic and antibiotics are giving on a long term basis. 2nd most common.
3. Cancer: Potentially life threatening, and unlike with humans its a very rare disease in dogs. Probably not why your dog's prostate is enlarged.
An enlarged prostate in dogs is painful with defecation because of the location of the prostate. When inflammed, it pushes against the rectum making it harder to defecate. Unlike with humans, which causes pain while urinating.
Treatment: The best treatment you can do is to neuter your dog, if a good candidate for surgery. If its a bacterial infection, long term antibiotics. Cancer...there is no cure and is very metastatic spreading to the lungs, liver, kidneys, etc.
Unfortunately, there is no special supplement or diet that you can give your dog to help with this...its all based on hormones. And since your dog is not neutered, I would bet on it being BPH. So neutering is the best solution.