Is obedience to one's mother obligatory regarding travel to the lands of the disbelievers and seeking treatment from a disbeliever residing there, under the pretext of not trusting the doctors in our own country?

Traveling to non-Muslim countries for medical treatment is permissible if certain conditions are met: security from temptation, the ability to perform religious rituals, and the unavailability of treatment in Muslim countries. Otherwise, it is not permissible. As for residing with a non-Muslim, that has other rulings. If travel is not permissible, then one must be gentle with the mother, apologize to her, and strive to complete the treatment in the home country.