How can one deal with an adopted Muslim girl who suffers from neurological problems and misbehaves, so that this does not affect the faith of her adoptive parent after his conversion to Islam?

A Muslim must realize that Allah is the Self-Sufficient, the Praiseworthy, and that the servant is poor before Him in all circumstances, including his need for worship and monotheism. His worship does not increase or decrease anything in Allah's dominion. He must also show kindness to people and thank them, for kindness is an absolute Islamic value, and preserving kindness, fulfilling good deeds, and thanking creation is part of thanking Allah. A Muslim should not make his religion dependent on people's kindness or their ill-treatment, nor should he disbelieve because of someone's harm or ingratitude. Religion is a relationship between the servant and his Lord, and every soul is responsible for its deeds, and no bearer of burdens will bear the burden of another. Also, this world is a testing ground, not a place of recompense, and the ultimate punishment is deferred. Finally, it is not permissible to adopt the girl you have been kind to by attributing her to yourself. If you cannot bear her harm, you may leave her to her own devices. Forgiveness, clemency, and kindness are the best stations for those who are able to do so.