Is it permissible by necessity to take an interest-bearing loan to purchase a home in a non-Muslim country, if the current housing is causing psychological and social harm that prevents the Muslim from performing their acts of worship, and affects their health, work, and their children's education?

The necessity that permits usury is when a person reaches the point of perishing or is close to it, or lives in unbearable hardship. Based on this, there is no license for the questioner to borrow with usury. He can move from his current location, and it is more befitting to migrate from the lands of disbelief to preserve his religion and his children. If he cannot migrate, then let him strive to preserve the rituals of his religion and his children, and that includes not dealing with usury except in the aforementioned state of necessity.