こちらは負傷者を一人抱えている
"We are carrying a wounded person alone"
or is it
"We have one wounded person?"
In the second case why 一人 is placed after 負傷者
こちらは負傷者を一人抱えている
"We are carrying a wounded person alone"
or is it
"We have one wounded person?"
In the second case why 一人 is placed after 負傷者
The latter, and there is basically no confusion (The first interpretation is not entirely impossible, but...).
To understand the strucutre, consider
こちらは負傷者をたくさん抱えている (We have many wounded person).
こちらは負傷者を n人 抱えている
I guess the placement has some freedom because the ひとり here works as an adverb.
You are right in that
こちらは一人負傷者を抱えている
is similar in meaning.
Your confusion can also be justified, as in:
(太郎は)悩みを一人[で]抱えている (He is carrying his worries alone = He doesn't open up).
I really can't seem to come up with a compelling and clear reason why the second interpretation is the only choice. Probably: