In my (admittedly limited) experience with tumors, there's not much you can do against the odor.
First you need to understand the state your dog is in. Tumors are bundles of cells that are physically and functionally changed (the medical term is "neoplastic cells" or "neoplasia"). A tumor "rupturing" doesn't mean it's going to burst open like a cyst, it means that the neoplastic cells are no longer able to survive and simply start dying (the medical term is "necrosis"). This is unavoidable and not the source of the bad smell.
The real problem is that the mouth is full of bacteria, which now find numerous niches on and in the tumor to grow to much higher numbers than normal. They produce the worst of the smell.
You need to be prepared that the state of your dog can change every day. Her body is still coping well with the necrosis and infection, but if the infection reaches the blood stream or overpowers her immune system, her state will deteriorate quickly. Please make plans for that unfortunate occasion in advance so your dog doesn't have to suffer until arrangements are made.
What can be done against the smell?
Your vet was on the right track with trying to kill the smelly bacteria with antibiotics, but antibiotics must be distributed via the blood stream. If necrosis set in, there is no blood reaching the outer parts of the tumor and bacteria are no longer inhibited by the antibiotics. A study found that antibacterial essential oils have a positive effect on malodorous tumors in humans. The full text is available here.
In an attempt to address this problem [of malodorous tumors], we have been conducting a pilot study in the use of topically applied essential oils. Essential oils such as tea tree and eucalyptus oils have recently gained acceptance as safe and effective antiseptics.
Their potent bactericidal activity has already been proven in in vitro and clinical trials.
We have previously reported that the elimination of tumor-related malodor is possible with an essential oil mix-ture, the application of which led to an improved quality of
life for our cancer patients.
Unfortunately almost all essential oils are toxic to dogs!
But the principle is clear: kill the bacteria growing on the tumor and the odor is improved. Please ask your vet for an antibacterial solution for dogs. Obviously it must be safe to be ingested in small amounts. Soak a cotton pad with the solution and wipe it over the surface of the tumor to hopefully kill some of the smelly bacteria.
Also, please consult your vet whether or not to continnue the antibiotics treatment.
