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.
Marriage is among the good matters that one should take the initiative to do; Allaah says (what means): {So race to [all that is] good.}[Quran 2:148]
So, it is not wise to delay marriage, rather obstacles should not be put to prevent it, especially in regard to girls because if they are advanced in age, no one would propose to them, and therefore, they would remain unmarried. There is no doubt that this causes sorrow and misery in this worldly life while much benefit is lost because of that.
Indeed, we have already clarified in Fataawa 84221 and 85252 that the criteria for choosing a spouse is religion and moral conduct as happiness in this worldly life and in the Hereafter lies in them. A husband who is religious and has a good moral conduct if he loves his wife, he will honor her, and if he hates her, he will not wrong her or insult her. Of course, it is permissible to seek other traits like money and beauty but one should not renounce religion and good moral conduct for these matters or make them a reason for delaying the marriage. All men who propose to marry do have some deficiencies and if a woman wants a husband without any deficiency at all, then she will probably remain unmarried.
Based on this, the best thing that your husband may do for his sister is to supplicate Allaah to facilitate marriage for her, and to try to bring her back as well as her guardian to reason. He should keep trying to convince them especially his sister because if she is convinced while her guardian objects and refuses those who propose to her without any sound reason, then she may take her matter to an Islamic judge or to whoever may act on his behalf so that he would marry her off if it is proven that her guardian refuses to marry her off without having a sound reason, as the ruler is the guardian for whoever does not have a guardian. Also, he may seek the help of rational and righteous people if necessary in trying to convince them.
Then, in case she is not married, your husband would have at least done what he is required to do but he should continue to give her advice.
As regards the people saying bad things about the personality of your sister-in-law, then your husband may use this as a means to convince his father and convince her. However, we warn against accusing a Muslim of any bad matter without evidence. Allaah says (what means): {O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin. And do not spy or backbite each other. Would one of you like to eat the flesh of his brother when dead? You would detest it. And fear Allaah; indeed, Allaah is Accepting of repentance and Merciful.}[Quran 49:12]
Allaah Knows best.