Is it permissible to obtain an interest-bearing loan from a European bank in order to move to an Islamic country, with the aim of saving one's children from religious and moral deviation, given that there is no other source of livelihood or alternative?

You must take the initiative to emigrate with your children from the country you reside in to the lands of Islam. As for borrowing with usury (riba), it is forbidden and only permissible out of necessity. So, if you know that you will not find a means to fulfill your needs and the needs of those you support, such as housing, food, and other necessities, then there is no harm in borrowing with interest.