Hello, my name isXXXXX and I have over 20 years of experience as a veterinarian. I am very sorry to hear about Bailey's urine and stool incontinence and trouble sitting down. Most likely whatever has lead to him becoming incontinent is also causing his difficulty sitting and is painful for him, though he is too stoic to complain much.
There are a few things that may be causing what you are seeing.
The first would be spinal arthritis which can cause inflammation of the spinal nerves that control urine and stool continence. These dogs have obvious spinal arthritis on radiographs and are painful upon examination. They may respond to anti-inflammatories (steroids or nonsteroidals like Deramaxx or Rimadyl), pain medications like Tramadol as well as omega 3's and glucosamine/chondroitin supplements like Dasuquin or Cosequin DS. You might discuss trying a nonsteroidal anti-inflammatory with your veterinarian to see if it is helpful.
If his urinary incontinence is related to weak urethral muscle function then medication such as phenylpropanolamine (PPA) can help that.
The second condition that could cause incontinence would be a degenerative myelopathy. This is a degenerative condition affecting the nerves of the spinal cord, it starts in the back legs and ascends eventually affecting nerves to the bladder and rectum which leads to loss of continence. These dogs aren't painful. They are incoordinated in the rear because they have lost the ability to feel where their rear legs are and place them properly. They become incontinent because they can not feel the stool building up and because their anal sphincter becomes loose. Unfortunately we do not have any good therapies for this condition. Radiographs look normal and diagnosis is by an MRI of the spinal nerves.
The other disease process would be lumbosacral stenosis and instability. This is an instability between the sacrum (pelvis) and the lumbar spine. It leads to inflammation and scar tissue and places pressure on the spinal cord leading to loss of function in his rear legs and stool and urine incontinence. These dogs are painful and should respond at least somewhat to steroids or anti-inflammatories. Diagnosis is by an MRI of the area. Treatment is surgery but once fecal and urine incontinence occur we cannot always reverse the damage done to nerves. Definitely worth trying though.
Unusual causes can also be a spinal cord tumor or a mass of the vertebrae or supporting tissues.
If he is an intact male, was ever used for breeding and is now running a fever Brucellosis is a possible cause as well, though less common if he seems to feel well otherwise and isn't running a fever.
A bacterial infection of the bones of the spine that spreads from a urinary tract infection or a puncture wound is another possibilty, but those dogs are running a fever and are extremely painful and feel horrible.
In order to help Bailey we really need to know why he is the way he is.
An examination and radiographs of his spine are a great place to start.
At that point your veterinarian can prescribe an anti-inflammatory and pain medication such as Tramadol and/or gabapentin if needed.
In the meantime it may help to increase the amount of fiber in his food to help him feel and be more aware of his stools. You can add 2 to 3 tablespoons of canned pumpkin or Metamucil to his meals to increase fiber. Make sure to get him outdoors frequently to pass stools as well so his colon is less likely to overfill causing stools to just drop out.
It may also help to add a glucosamine/chondroitin product (examples are Dasuquin or Cosequin) and an omega 3 fatty acid (like 3V Caps or Derm Caps). These worksynergistically and improve cartilage health and joint fluid quality and quantity as well as reducing inflammation. They can take several weeks to see full improvement but some dogs do very well with them added. They are available over the counter.
Another option is a product called Duralactin. This is an anti-inflammatory product derived from milk proteins and it also has omega 3 fatty acids incorporated into it which can be very helpful. See this link for further information: http://www.duralactin.com/products_canine.htm
Other alternative therapies such as cold laser, acupuncture or chiropractic may be of help as well is his problem is arthritis related.
Let me know if you have any further questions.
I understand mom's concern completely.
If we can control the inflammation, and thus improve his continence, and get him pain relief then she doesn't necessarily have to take that step yet. It all will depend upon his response to medication. Sometimes nothing we do helps and it becomes unsanitary for the pup and the family, but many times we are able to buy them some comfortable time with medication.