OP, good luck on this.
I will be blunt so please don't take offense - I'm stating guesses strongly, just to give you something to think about. You're the boss of you.
As a reader, it sounds like you and her are on different tracks, but you agree that her $ is hers and your $ is yours. So...
At some point, you either do whatever the hell you want with your pocket money that's less than hers, or you continue accepting her requirements even though you don't like them. Obviously it's better to persuade and communicate if satisfaction for all can be obtained through such gentle techniques, but you both seem to have already discussed this and formed positions. Her position according to you is "embarrassed if you don't work at your nice PhD job that impresses mom"; both of you have the position that her money is hers and gives her power; your position is you hate work but don't want to quit without permission. Now it's possible that the Lifejoy path will work (her post is genius; read it!), and it's possible that more discussion will elucidate a peaceful path to agreement between you and Dear Wife, even if wife joins you in flipping her mom the bird. But I think it's likely from your description that change will only occur if you rise up from your mental chains and act.
Pull a Bartleby the Scrivener and don't work any more. Do it suddenly or tell your wife it's coming. There is no telling what will happen, except that it will be different. Just be aware that since you are changing the terms of your marriage, you may end up divorced.
I don't think that's the worst outcome necessarily. I don't think it has to happen. But most likely, your wife won't back down until she knows you are committed to change come hell or high water. My first thought is that you should prepare for the divorce contingency, establish a target date for quitting, and tell your wife you plan to quit. Then listen to the freaking out, take all threats as emotional expressions rather than permanent positions (again, don't argue - just listen), stay calm, and gradually determine whether you two can coalesce around a new you. The coalescing can only happen if you stick to your new direction, though.
If you want to warm up to this for a year, start living a life where you rely only on your own funds. One year of succeeding in this will prove to yourself that you don't need her money. After that, you are free and should act accordingly.
Yes, your plans need to include a fair share of parenting. Yes, my comments are harsh (simply because it sounds like that's a perspective you sound like you need for your own reference). No, FI at your individual stash level as a parent won't be easy without a job - that's why I suggest trying it for a year.
Can you negotiate a sabbatical leave any time soon? That's a great time to live cheap and practice being jobless.
It's preferable for all parties in a marriage to agree. That isn't happening yet. At present, you are unhappy while everyone else won't listen, if I read your remarks correctly. It's going to be up to you to change this deal and yes, that probably means walking away. If not from the marriage, then at least from the present version of it.
If your kids are young, you've got to fix this now, before they grow up thinking "Dad" means "Sad Sack."
PS. The other option is dig into why you hate the job. If somehow the emotions are similar to those at home, some combination of counseling and increased assertiveness will probably be needed no matter what you do. Perhaps facing the emotions there and working through them (so to speak) on the job would be better, especially if you discover that you are not FI on your own funds. If you're not actually FI on your own, you will need a job anyway. Only you can decide which path to explore first. Or whether to explore each path. But do something!!