Welsh mother, Iraqi Dad: Welsh-Iraqi / Iraqi-Welsh? Or no difference?
After a quick bit of googling on Irish-American, my understanding is that you can write:
- He is an Irish American
- He is Irish-American
In the former, "American" is a noun, and Irish is an adjective; it means an American with Irish ancestry. In the latter "Irish-American" is an adjective. But I suspect the common order of the two nationalities in the adjective follows the adjective-noun order.
As you're written "Welsh-Iraqi" and "Iraqi-Welsh" you're presumably looking for an adjective. I suggest that you need to decide whether you are talking about a Welsh person with Iraqi ancestry (which would give you Iraqi-Welsh) or an Iraqi person with Welsh ancestry (Welsh-Iraqi).
How you decide whether a person is "primarily" Welsh or Iraqi I don't know. Perhaps based on citizenship. Or perhaps, as mentioned in a comment by Steven Littman, it would be based on where ther person lives.