Actually - as a vet, though sadly an unemployed one because of my CP and related problems, - yep, tramadol is quite often used as a pain killer in dogs. One situation is as a home palliative in canine cancer patients - obviously we have access to euthanasia in animals when pain becomes uncontrollable, so heavy duty narcotics are not appropriate in the veterinary context as they are in the human one. Another is the one you've mentioned - to manage joint pain, especially for ongoing pain in an older animal.
If it's a joint problem as against a bone problem causing her pain, ask your vet about injections of a drug called pentosan. It's believed to work by maintaining cartilage and encouraging joint fluid production. It might also be worth thinking about putting her on a glucosamine supplement...they're really not much different from us.
Most of the drugs are the same - I've even (doing my clinical training in a referrals clinic) used gabapentin for managing neuropathic pain!
CRPS since 1999, diagnosed in 2005 and since spread to full body, spasms, dystonia & contractures, gastroparesis, orthostatic hypotension,bradycardia/tachycardia, bone spurs, bursitis, carpal tunnel syndrome.
On Oxycontin/Endone, Topamax, Mobic, Magnesium, Florinef, Midodrine, Somac, Cipramil. Have a spinal cord stimulator, intrathecal pump with baclofen & bupivacaine and doing physio.