Howdy Again
I don't know if your Dad tried to fire that 38 Short Colt ammunition in that gun, but it is the wrong cartridge for that gun. Old cartridges can be very confusing.
In this photo, a 38 Short Colt is on the left and a 38 S&W is on the right. If you look closely you will see the bullet of the 38 Short Colt is the same diameter as the cartridge case. That is because it uses a heeled bullet. The 'heel' is a short section of the bullet at the rear that is the same diameter as the
inside of the cartridge case. This is an old type of cartridge, the only ammo still commonly made that way anymore is 22 Rimfire ammo.
The 38 S&W uses a more conventional bullet that is the same diameter as the inside of the case for its entire length. You can see the difference. Bottom line is, the bullet on my 38 Short Colt cartridge is .372 in diameter. The bullet of a 38 S&W cartridge is usually more on the order of .360 in diameter. This one happens to be .356.
I just tried to chamber a 38 Short Colt into the S&W 38 Double Action I posted earlier. Because the bullet is too large in diameter, the cartridge will not seat all the way. It bumps into the chamber throat and the cartridge will not seat by about 1/8".
The correct ammunition for that revolver is 38 S&W. As I said before, 38 S&W, not 38 Special. However I will further caution you that I do not recommend firing modern ammunition in a gun that old. Others will disagree with me, but the steel in those old guns is not very strong, and modern Smokeless ammunition creates a pressure spike that the old guns may not be able to withstand.
Best you keep the gun as a memento of your Dad and not try to shoot it.