Is it permissible to use money designated for orphans' charity ($15,000) to complete the purchase amount of a house for the family, given that buying a house achieves stability for the sake of the religion in the new country of residence?

If your intention was merely to give charity without making a vow, then it is permissible for you to take the money and buy a house with it, because charity does not become binding until it is seized, according to the majority of jurists. However, if the wording constituted a vow to Allah, then it must be fulfilled.