Carol,
My heart goes out to you. It seems to me that the doctor's suggestion is wise. He is saying that IF the radiologist agrees that it would not be harmful, the low dose radiation would provide relief for your mother. The trach tube and PEG are not pleasant to see but as someone who had both for a while I saw them as alternative means of the basic functions of life, breathing and eating. Instead of guessing and worrying, ask the doctor why he is recommending them.
You have not mentioned her primary doctor. I would certainly recommend getting his opinion as well as that of any other physicians she is seeing. Ask the ENT to forward results of his diagnosis and the CT and PET scans to them for their records.
Until the results are in you really are in limbo. You are making assumptions based on fear and love of your mother. Is there anyone you can talk to whose judgement you trust to help you through this.
My prayers for your mother and for you.
Malka