You must know why your in-laws quarrel before you want to comfort your husband, and only by figuring out the reason can you really go to solve things. I think your in-laws have a pension at this age, so they shouldn't be fighting over money. Most of their fights should be due to the fact that the two of them don't get along with each other. Because your in-laws are from the 50's and 60's, it was not free love at that time, marriage was arranged by parents, so the foundation of their relationship was weak.
That time the two people do not understand each other under the premise of marriage, after marriage only to find that the two people's personality differences are so big, and the more you live the more you feel the other side of the incomprehensible, so it is always quarrel. I think your husband did not suffer from this kind of pain when he was a child, and it is likely that he grew up in a quarrelsome environment.
I think you can relatively reduce the number of fights by just distracting them. You can let your in-laws to do something they want to do, such as nowadays the old people like to dance or learn some embroidery crafts, etc. As long as they have something to do, they will not always fight. As long as they have something to do, they won't fight all the time, and your husband won't feel so miserable.
You can also comfort your husband to be a little more open, after all, they are old quarrel will not be as intense as the young people, and may not be they want to quarrel, just that they have been arguing for a lifetime are noisy habit. Or you can bring your mother-in-law to your home to live, as long as the two of them separate and calm down a bit, maybe a little better for the fight.
You can also advise your father-in-law that your son is suffering a lot because of your quarrels. Even if you don't look at your mother-in-law, you should try to give in to your mother-in-law for the sake of your son, otherwise it will hurt your son's feelings too much.
You can also let your husband take your in-laws out for a trip, without going too far to the neighboring scenic spots. This can ease their family's feelings, your husband also took the opportunity to take a break, not too depressing.