a. I was driving around in my car with my brother.
Does that imply that I have only one brother?
b. My sister's co-worker's husband is an engineer.
Does that imply that my sister has only one co-worker?
c. My father's cousin's husband is a dentist.
Does that imply that my father has only one cousin?
I think from a grammatical point of view the answer to all the questions is 'yes', but in practice the answer might be 'no' because people in this particular case there is a lot of sloppiness around!
I might be wrong of course.