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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
First of all, we congratulate you on the blessing of embracing Islam, and may Allaah reward you for your keenness to constantly obey Allaah. We ask Allaah The Almighty to protect you and guard your religion.
If the case is as you mentioned, that it is difficult to practice your religious rituals in the country where you live, you must migrate to a Muslim country where you could be secure about your religion. The opportunity you mentioned in the question facilitates your migration matter; in addition, it is a good thing that your mother wants you to travel to study there. For further benefit, see Fatwa 86405.
However, you have done well by your keenness on being dutiful and kind to your mother. Dutifulness and kindness to your mother is possible even when you are away from her by calling her and investigating her matter, or doing any action which may serve that end. The same applies to your sister. For further benefit on this issue, refer to Fataawa 82254 and 87019.