All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
If the situation is as you mentioned, namely, that your parents are in no need of you and leaving them will not adversely affect them, then, there is no harm in travelling for this noble purpose (earning a living) even if your mother does not agree. The Muslim jurists stated that if a person wanted to travel for trade or to perform Hajj or `Umrah or a similar purpose but his parents disliked it, while he does not expect that his absence will affect them adversely, then there is no harm in travelling. They said that the reason is that these journeys are often safe.
If, in addition to earning a living, there is a nobler purpose, namely, living in a Muslim country, learning Arabic and sciences of Sharee`ah, then the permissibility of your travel is even more confirmed.
Nonetheless, you have to do your best to please your mother in every possible way and offer that she and your father accompany you so that you can take care of them.
For further benefit, please refer to Fataawa 86405, 82254 and 84942.