It depends how the exercise was presented:
Dictation in French: "son" is most probably "her" husband
Marginally, it could also be "his husband" (Isabelle doute du mari de Pierre). But in France, please wait a bit since mariage between people of the same sex has been legal only for a couple of months ago!
- extra meaning: even with "her husband", it could be another woman's husband (Isabelle doute du mari de Jeanne). Context would tell.
Written French for translation into English: see above
English text for translation into French: only "her" (+ extra meaning)
"Doubt" can be either a verb or a noun.
If used as a noun, you would say "She has doubts about her husband" or perhaps "She has a doubt about her husband"
If used as a verb, you would say "She doubts her husband".
The verb is conjugated so it's like this:
I doubt my husband.
You doubt your husband.
She doubts her husband.