Is the mother sinful if she expels her two daughters from the home for refusing to travel with her and leave the trust [Amanah], and are the parents sinful if they leave them alone?

As for the married daughter: You must advise her regarding the impermissibility of seeking divorce without a valid reason, and the impermissibility of abandoning the marital home without an excuse. If she does not have a safe dwelling, she must not be expelled.

As for the youngest daughter: She must not be expelled if she does not have a safe dwelling.

As for leaving one or both daughters alone: If it exposes them to corruption, then it is impermissible, and you are responsible for them and for their protection. Either abandon the journey, or house them with a mahram or a righteous woman.

Residing in infidel lands: This entails risks to one's religion and morals.