Amasashi, I agree that this would be really annoying, and maybe when dating should have been a dealbreaker, but I think Chey makes some good points too, certainly in the “don’t expect her to change” department, and also that she has attributes you admire. Most of us who are married have some things in our partner that would once have been a dealbreaker that we learned to work around.
Practically the way I might deal with it would be to (1) save money when I could and just don’t bring it up with her, (2) be a little slower to open your wallet, and (3) also be thankful for the benefits you get from her. On 1, some couples just operate this way. I don’t love it, but if her approach is “I’m going to keep what I’m going to keep,” then you probably can do the same without guilt. Maybe someday you combine the pots together, but for now maybe it’s a wall you leave up and just live with it. Try to save a little every month, possibly in your home country. On 2, it’s hard to tell if she wants you to be the big spender or what. I’d definitely get to know the in-laws more, because this is probably something she grew up with. Try to understand what she’s thinking, but also feel free to forget to bring your wallet or pick the biandang place over the fancy place. On 3, you say you’re both working, so if her parents or others are helping you on childcare or rent, just be really grateful. If it were my partner and my kid, I’d be willing to live with some inconsistencies and irrational behavior and even some selfishness if I could contain the bad-behavior and put in some safeguards. On the positives, she doesn’t seem wasteful with the money and she is bringing in a full income. Taiwan is also funny because it doesn’t seem to make it easy to have joint accounts. In practice it sure seems like you only get one name on the card.
I’d keep reading up, both on finances and relationships. I like the bogleheads website for longterm investing. Ironically, there are a fair number of questions there about relationships. This is a good group here too.