Wait wait what?....

Your wife, is willing to allow her OWN kids to go hungry, while she is sending away ALL her money to her parents?????

I mean I get family obligations, my culture is pretty big on it too, but that is just pretty *****ed up.

No amount of tradition or culture or obligation explains this "logic" of hers.

Who's responsibility are these children exactly?
Apparently not hers, IMO she shouldn't have had any children if she was unwilling to assume responsibility for them, if she was willing to put her parents before them.

It will be a cold day in hell before I put anyone else before my daughter.

I have no clue how you're supposed to resolve this issue when she so clearly is disinterested in resolving it, her priorities are misguided.

What I would do though?

Stop paying her bills, whatever she charges to her own credit card is HER problem, if its her money like she says, its her debt too.
End of story