I don't see any problem with either Method 1 or 2. As long as your wife is eligible for a Roth IRA, how and where the money came from to fund the Roth IRA is irrelevant.
I'm curious as to why you and your wife are opening a Roth IRA since both of you are here on a temporary visa? Roth contributions are not tax deductible. While it's true that withdrawals after 5 years could be tax free. But will you and your wife be in the U.S. by the time you can withdraw the funds tax free (reaching age 59½)? If you will be back to your home country by then, what is the benefit of contributing to a Roth IRA? Your home country may tax you for the withdrawal. No need to answer my question. Just something for you to ponder. Good luck!
