Who has a cold, "she" or "her mother"?
If the subject of the sentence, "she," is the one who has the cold, then you should say "She went to see a doctor about her cold with her mother." because it is clear that "she" is the one who has the cold, not "her mother."
"She went to see a doctor with her mother about her cold." is a little more awkward. In this sentence it is impossible for the reader to know whether "she" has the cold or "her mother" has the cold. Also, I don't think that this version flows as well.
Another possibility which is grammatically correct is "She went with her mother to see a doctor about her cold." But this sentence also has the problem that we do not know which of the two people has the cold.
Thanks Bioche but you have changed my sentence.
I want "with her mother' in my sentence.
Thanks nm. Your analysis helps me a lot. And I recognise that it isnot easy to put a prepositional phrase.
She went with her mother to see a doctor about her cold.
This feels the most natural to me, but it is very unclear who has the cold.
With her mother, she went to see a doctor about her cold. This flows less well, but is more clear. I prefer it over your #1; I cannot decide whether it is better than your #2.