Is it permissible for me to prevent my two daughters from working and studying in mixed environments, and what should I do if they run away from home, knowing that their father is remiss in providing for them?

The parents of the two girls must prevent them from working and studying in mixed-gender environments, especially if they show recklessness and converse with males. They are accountable before Allah for their charges. They must prevent them from going out, and commit to advising and guiding them, reminding them of the obligation of hijab and staying at home, and seeking help from books, tapes, and sermons. However, if preventing them would lead to their running away and falling into bad company, then they should not prevent them. Instead, they should continue to advise them and supplicate for their guidance. This falls under the principle of choosing the lesser of two evils.