I am glad you contacted me, making this decision can be tough and you need to make sure you have all the relevant information first. Cancer is the most common disease in older dogs however many masses arent tumours and many tumours arent cancerous. How does your vet know it is a tumour? Have any tests been performed? We cant assume that just because your dog is 14 that a cure isnt possible.
I would recommend as a minimum a second opinion. At the least a non-surgical biopsy called a fine needle aspirate should be performed. This test is painless and most of the time tells us exactly what the mass is and then plans can be made from there.
Even if the results come back as an aggressive tumour not responsive to surgery, saying goodbye may be premature. Even if your dog is in pain, if she is eating and still enjoys a scratch behind the ear then she is not suffering and keeping her with you and spoiling her rotten would not be a bad idea.
Let me know of any more info you have but it sounds like you are right to want more information before making such a permanent decision.