Sentiment analysis probably isn't the right option here, though it may work.
I think a combination of dependency parsing[1] and regex is the way to go.
regex examples: "Remote: No", "No remote please"
Dependency parsing examples: ""Remote work isn’t an option", "Remote work will not be considered"
[1] look for negation in the parse tree using something like http://demo.ark.cs.cmu.edu/parse?sentence=Remote%20work%20is...