In my experience, most managers are well-meaning people who try to do the right thing for their employees. If so, actions 1-4 above should help you address their concerns and be more successful in negotiating for flexibility.
However, there are jerk bosses out there as well. Some don’t believe that “family stuff” and workplace flexibility are legitimate concerns. Some feel as if they paid their dues by sacrificing their personal lives for career success and they’ll be damned if others won’t have to do the same. Some see “involved parent” or “family man” as derisive terms.
Honestly, it will be very difficult to negotiate with someone who is openly hostile to flexibility. Worse, working for a boss like this makes for a stressful worklife that also spills over into our home and personal lives, hurting our mental and physical health. So, my unsatisfying advice for those in this situation is to keep your head down for now, do a great job, network widely, and fire off resumes to other employers. If you have the opportunity to leave an aggressively unpleasant boss, please do.