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.
If you mean that your father-in-law is angry with you because of not answering his request to meet the husband of his sister, then he should not have got angry for that reason because you are not religiously obliged to accept his request even if you had no reason, let alone if you already have a sound reason for that.
Therefore, we advise you to be wise in solving this problem, and you should clarify the matter to him as he might have misunderstood the way you behaved. You may also seek the help of whomever you think might influence him so that he would be able to reconcile between you and him. This is what you should do with anyone whom you think is angry with you among your in-laws.
In fact, problems between the in-laws might lead to many negative effects and keeping good relationships between them is something religiously required as clarified in Fatwa 125843.
Allaah Knows best.