Will the questioner and his family be saved from sin if he accepts gifts and food from his brother-in-law, who works in a bank, then secretly estimates their value, takes that amount from his own money, and donates it to the poor, in order to avoid disagreements with his wife?

If all or most of your son-in-law's income is from unlawful (haram) sources, or if what you receive from him is the very unlawful money itself, then do not accept anything from him. You must explain the unlawfulness of this to your wife, for pleasing Allah takes precedence over pleasing people. As for what you accepted previously and spent it on good deeds, that is commendable. However, if your son-in-law's income is a mixture of lawful (halal) and unlawful, there is no harm in accepting his gifts, though refraining from them is more cautious. It is advisable to counsel your son-in-law and explain the danger of what he is doing.