If the gun shoots to the sights then leave it alone. It will also have more sentimental value as your dad's gun if you leave it as it is.
If the gun has the half-moon sight it was made before about 1952, when all S&Ws were still referred to as "Named Models" It is not a Model 10 anything but what is often referred to as a Pre-10 (incorrectly). Properly it is a .38 Military and Police. Model numbers were not assigned until 1957, and not generally seen on the guns until 1958 and later. It was even later before the first "dash" numbers were added, which indicate changes to the basic model. Model numbers did not replace the model names, but were in addition to the name.
If you do insist on "fixing it" the easiest and probably cheapest way is replace the barrel. Many times one can be found on E-Bay, but I wouldn't do it!
How much high does it shoot, and at what distance? You can either shoot lighter bullets or simply hold under that amount. If our dad was serious about target shooting he was probably shooting .38 148 grain "mid range" wad-cutters. Try those and see what happens. Remember your eyes are different than his, you may see the sights differently, and you may be using a different hold on the target than he used.