Nice of you guys to blame it all on the wife. First of all, it is a no win situation. Even if she new which questions to ask and where -and she doesn’t, because she is not a foreigner, has never been through the ropes like us, and probably knows no one who has -so even if she the asks in perfect Mandarin, she will get different answers from different officials. Officials are not here to help you. It is in their best interests that you do not settle here. They have enough brown people/foreigners and everyone knows we are not to be trusted, we are not Han. You marry to steal our beloved seeds.
Remember the good ol days when people could only stay if they got married, and foreigners had no working rights? That there was no way a white face could get the green ROC passport? Many people live still in that era, but even then, you could get an ID under the table if you knew the right people. Otherwise, forget it. So give a bit of leeway to your partner, who, raised as a Taiwanese, thinks in giving authority to other people and follows mostly blindly and has no idea to contest or questions the establishment. If her Uncle Hou told her to do X she will do as told. And ask of push at the authorities, being NIA or BOCA? Unthinkable. Most of all, they probably think that if they know Official Wang or Secretary Yu, then they can get things done anyways. If they do not know anyone who can help, then that is a loss of face and hence also a no go.
Moreover, when they settled/visited/worked/stdied in a foreign country, they probably were subject to a standard issue procedure. They may think it is the same all over the world and then blame you for being unreasonable and uncooperative. No fun as a pet anymore.
Finally, yes, it can be a bit of a power play. Maybe they do not really want to help you achieve all your rights because then the balance of power will be upset. Most Taiwanese do have the experience of a foreign partner in the form of a mail order bride, bought and sold almost like cattle and with about the same rights. A disposable womb. Then if they look down on you as a person and as a partner, they will keep you under their foot one way or another. But if that is the case with your relationship, you have bigger problems and you have more urgent things to do than to engage in a childish power struggle. Your future and your soul are at stake here. In that case, I would advise you not to waste a single day and cut your losses/start over. Just make sure you do not leave any children behind.