Pictures would help if you can post some. Lots of things can cause tomato leaves to turn yellow. Do they have other symptoms? curling? holes? brown spots? What did you mean by branches "appear to be dying"? What is happening to them to make them appear to be dying?
Unfortunately both under watering and over watering can cause yellowing. But you soil condition should tell you that-- is the soil wet or dry? Tomatoes like even moisture, they don't like to dry out or to stay wet.
Nutritional deficiencies including not enough nitrogen, iron, or calcium can cause this. If you think it might be under-fertilized, try fertilizing with a good nitrogen source, ironite, and bone meal or epsom salts and see what happens. I don't think over fertilizing would cause this.
Otherwise, especially if the leaves are curling or have other sx, it may be a bacterial, viral, or fungal infection. One of the commonest in tomatoes is fusarium wilt. You can google that and find a picture, see if it looks like what is happening to your tomatoes.
Best wishes, I know it would be heartbreaking right now to lose your dad's tomato plants-- sorry for the loss of your father.