Is returning to Muslim countries—to avoid tribulations and the difficulty of living in Western countries—considered a sign of a lack of patience and faith, or is it obligatory to be patient until sufficient money or a job opportunity in an Islamic country becomes available?

It is not permissible to reside in countries where one fears for one's religion due to temptation (fitna). If the circumstances of your home country are not suitable, then seek another country to reside in to safeguard your religion and the upbringing of your children. This emigration will be a proof of your patience and faith. As for remaining in countries of temptation, it indicates a deficiency in faith and a lack of patience.