Is it permissible for me to travel abroad for work to increase my income, or must I stay with my elderly mother and unmarried sisters? And would I be sinful if I travel, given that procedures have been facilitated after performing Istikhara?

If you do not fear destitution for your mother and sisters, then you have the choice between travel and staying to care for them, and the preference is based on what serves their best interest. If there is a benefit in traveling, such as seeking lawful sustenance, then traveling is more preferable and there is no sin upon you, for Allah Almighty says: ﴿There is no blame upon you for seeking bounty from your Lord﴾ and ﴿It is He who made the earth subservient to you, so walk among its regions and eat from His provision. And to Him is the resurrection.﴾ However, if it is easy for you to seek sustenance in your country, and they need your presence, then staying with them is more preferable.

If you decide to travel, it is desirable to seek permission from your mother and siblings and to please them, but this is not obligatory unless the journey is dangerous. For a safe journey for trade or similar purposes, the consent of parents is not a condition if you do not fear destitution for them, as mentioned by Imam Al-Sarakhsi Al-Hanafi. And it is stated in Al-Bahr Al-Raiq that there is no harm in traveling for trade or Hajj without the permission of the parents because there is no fear of perishing in it.

If you do travel, you must keep track of their news, provide for their material needs, and visit them whenever possible.