I googled the question, does Islam require people to support family overseas and there are many links. I got this from one of them:
"1) Male relatives, such as one’s brother, uncle, nephew, etc. The responsibility of financially supporting them is only in the situation where they are poor and not capable of earning themselves due to some disability or illness. Imam al-Mawsili (Allah have mercy on him) states in al-Ikhtiyar:
“The Nafaqah (financial support) of other relatives besides the parents and children is (also) necessary according to the amount of inheritance (mirath)….And this is only necessary when the relative is poor, disabled and not able to earn.” (al-Ikhtiyar li Ta’lil al-Mukhtar, 2/232)"
If the brother and wife are foreigners to Turkey and haven't been employed there for a year at least, they will not be entitled to benefits.
I then googled health service in Turkey:
"Is health care free in Turkey?
Is healthcare free in Turkey? Yes, to the extent that a universal healthcare system ever is. The Turkish government pays for healthcare through taxation, and it covers all the scenarios and treatments listed above. If you're a resident with a job, your employer will even pay your insurance premiums."
Brother needs to work and provide for his wife, child and himself.