Meals and Incidental expenses (for Dubai)
There are two issues here, one being the IRS/taxation the other being INS/greencard.
I suggest commuting back and forth back to the US every six weeks, therefore the greencard issue is no longer a concern. You would still be a US resident.
What remains is the IRS issue. By commuting you will blow through the 35 day limit very quickly but I believe you may be able to deduct the M&IE's (meals and incidental expenses)on your tax return.
M+IE's are calculated by the IRS for all American cities and for many international destinations. If you take the rate for M+IE Dubai per day and multiply it by the number of days you spend here then you should have a fairly healthy tax deduction to offset any income tax you pay from living in the US for 1/2 of the year.