Is a woman's desire to stay home and not work, her refusal to mix with men (non-mahrams), her lack of pursuit of financial independence, her lack of ambition, and her fear of divine accountability for knowledge not acted upon, considered deviant and dependent thinking from a Sharia and social perspective, or is her family's objection based on a misunderstanding?

The questioner's opinion is correct. A woman's work is permissible as long as it does not involve prohibited mixing (where 'awrat are exposed, physical contact occurs, or it incites fitna). As for permissible mixing, which is free from the aforementioned prohibitions, it is allowed. Islam encouraged women to remain in their homes and not to go out except for a need. In fact, it made their prayer at home superior to their prayer in the mosque, and their great role is the upbringing of children. As for seeking knowledge, if it is an individual obligation (fard 'ayn) (like the obligations of Islam), then it is mandatory. If it is a collective obligation (fard kifaya) (like the presence of a scholar or a doctor), then if some people fulfill it, the sin is lifted from the rest. The teaching of knowledge is not obligatory for everyone; if enough people undertake it, the sin is lifted from the rest.