The easiest way to tell would just be by holding it and assessing the weight. That model would be a full gold case and bracelet and would be considerably heavier than any other watch you've ever held.
If you see any parts of the bracelet that have the gold plating worn through, that would indicate it's a rep.
Why would your father have and give away a $20,000 Rolex that you didn't even know about? And, most people would have kept the box and papers on something that valuable.
My guess is that it's a fake, based on almost all gold Rolexes come from the factory with a champagne date wheel, while that one's white. Also the gold color doesn't look near right, but that could be your camera.
Did you have the gold tested? Is the watch 18K? Looks like an older model President w/ diamonds, but hard to tell if real by your pics alone ....
Older models would have lug holes and President models were all DayDates. But that has the newer style bracelet.