I've read cultural gems in the 7 pages of this topic. To answer OP, I believe a mix of finding out what the real traditions are (yes the girl do marry OUT of the family) and communication on the his wife's insecurities, along with a good deal of smart accounting and shared accounts should settle this down in happiness.
As i finish reading this topic, I'd like to point out how it work with "my in-laws":
I lived in their house for over 3 months last year. As i did not have income per se (I was a student and was getting money from my own family), they refused even to consider the idea of me paying for anything. Their lifestyle included going to nice restaurants 3 or 4 times a week, a 4 days luxury new year trip with the extended family, frequent travels to Kending in the best place over there...
They are a rather traditional family living in a small town in the south. I would consider them as traditional but rather educated.
They actually paid for the trip expenses of the uncle and his wife, who also happen to have used their car for the past 4 or 5 years. He lent them extensive amount of money when their business was short of cash and cash seems to go back and forth between the two families (albeit i, my girl, and the younger sister are lobbying for a bit more accountability). Another uncle screwed the rest of the offspring when the grandfather died on the pretext that he was the first son. He has been literally erased from the family tree and the two sisters made it up to the second son with their share of the heritage.
The younger sister has been giving her entire income to the family for the past two years (she lives with them), they are now thinking to buy her a car. She is soon going to be managing one of the uncle's buxiban. My girlfriend (she has lived with the family until now) has been using her income to buy life insurance and to start invest, in her own name.
My girl's older sister, who has been managing the family business in Taiwan for the past 10 years, has been paying every single expense of my girlfriend's education in the US and UK. This includes 2 years language school in the US (where we met) and 2 years to pass her master in the UK. She is frequently having issues with her father over his management of the family's business in China (he has poor notion of cash flows and getting paid on time). She extensively helps people in her Guanxi (albeit once again, we are trying to influence this to make it more reasonable).
Under these conditions, and since there is no son in the family, I would be more than eager to help them cope with hardships, or subsidize the younger sister's foreign diploma if we were married. This would come with ties over how they use this money, but I do consider it perfectly normal and fair to help the family in these conditions.
My point is that while money can be an issue, these people are family, and we should not forget it.
It is also quite often easy for one to see what efforts one may be doing in the direction of the other's culture, but that may as well blind one in thinking he is doing the most. A bit of lucid generosity (mostly intellectual one) is necessary here.