If the terrorists only want Turkey to break ties with Israel and the USA, don't give the terrorists what they want. Breaking ties would hurt the economies. IHH is a terrorist islamist group which is anti-western and the islamist extremists have stated they want Turkey to break its ties with Israel and the West. This would only hurt Turkey and so terrorist groups shoot themselves in the foot by hurting their own people.
U.S. House Speaker Boehner brushes off call for his ouster (Reuters)
from the article: Turkey sets up own Gaza flotilla inquiry