How can one deal with a foul-mouthed father-in-law who speaks of matters that cause embarrassment, and the husband cannot deter him for fear of his anger, knowing that he is an old man? And how can one overcome feelings of animosity towards the in-laws?

There is no blame upon you for your feelings towards your in-laws due to the bad character of one of them. However, you should not show this to them or to your husband. Rather, treat them kindly and overlook their shortcomings. Your husband should advise his father gently to stop his bad behavior, which contradicts the perfection of faith and exposes its perpetrator to Allah's hatred, for "the believer is not a slanderer, nor a curser, nor an obscenity speaker, nor one who uses foul language," and "nothing is heavier in the believer's scale on the Day of Judgment than good character, and indeed Allah hates the obscene and foul-mouthed," and "indeed, Allah does not love the obscene and foul-mouthed person."