Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, thank you for having confidence in us and we pray to Allah to grant you a better solution for this problem and ease your burden for you in this world and Hereafter, amen.
As for your question, we'd like to state that in Islam it is not permissible for the guardian to compel the one under his guardianship to marry someone she does not desire to marry. Hence, your mother has no right to force your sister to marry against her will and you incur no reproach for what you did; there is no sin on you as you do not want to force your sister.
We recommend you to explain this to your mother and point to her that Islam does not permit compelling women to marry against their will and that enforcement will render the marriage contract invalid.
Elaborating on this issue, we'd like to cite for you the following: "It is not permissible for the father or someone in his place to compel the one under his guardianship to marry someone she does not desire to marry. Rather, it is necessary to seek her consent and permission due to the hadith of the Prophet (peace and blessings be upon him) that states: “The virgin is not to be married until her consent has been sought.” They said: “O Messenger of Allah! What is her consent?” He replied: “Her silence means consent.” And in another wording: "And regarding the virgin, her father seeks her consent and her consent is her silence."
Therefore it is obligatory upon the father to seek the consent of her daughter before marrying her off. This rule also applies to everyone who happens to be a girl’s guardian, because one of the conditions of the marriage in Islam is the consent of both parties. So if the marriage is arranged without meeting this condition and the lady feels unhappy with the issue, such marriage is not valid.
It is required from the prospective husband, when he knows that a girl does not want to marry him, not to pursue the matter even if her guardian facilitates this for him (give him permission). It is obligatory for him to fear Allah and not to approach the lady who does not want him.
Also, it's quite relevant to mention here the hadith narrated by Ibn `Abbas that: "A girl came to Allah’s Messenger (peace and blessings be upon him) and said that her father had forced her to marry someone. Thereupon, Allah’s Messenger (peace and blessings be upon him) gave her the choice of either accepting the marriage or nullifying it.” (Reported by Ibn Hanbal) In another version, the girl said: “Actually, I accept this marriage but I wanted to let women know that parents have no right (to force a husband on them)." (Reported by Ibn Majah)"
Excerpted, with slight modifications, from: http://www.themodernreligion.com/index2.html
