Dad had prostate cancer 20 years ago and had his prostate removed. He now has recurrent prostate cancer, but the urologist assures me his bladder is emptying. I take him to the toilet every 2 hours throughout the day, until bedtime. I make sure Dad has his coffee in the morning early, and about 2 full glasses of water before 3pm. I give him about 4 ounces of water with his evening pills at 4pm, and NO MORE liquids after that. I'm baffled. He gets up once or twice each night to urinate. In the morning I discover sometimes the bed chuck is wet, and his disposable brief is soaked. Where is all the pee coming from?? The expense of disposable briefs and guards is outrageous. He goes through 6-8 guards a day in spite of being taken to the toilet.
And it certainly doesn't sound like your dad is getting nearly enough fluids in his system, if he's only drinking coffee in the morning, 2 full glasses of water before 3:00, and only 4 oz. before 4:00 p.m. That is not nearly enough to keep your dad hydrated.
I know you don't want him peeing all the time and wetting his diapers(even though that's what they are for and he can't help it), but dehydration in an elderly person in particular is much more dangerous than him peeing all the time.
So I would give him plenty to drink during the day with a cut off time no later than 7:00 p.m., and then if you don't want to continue taking him to the bathroom every 2 hours well into the evening you may want to think about using a condom catheter on him overnight, so you and he can both sleep and he won't wake up wet.
You can also talk to his urologist about perhaps putting him on an active bladder medication as sometimes those help and sometimes they don't.
Sometimes a change of position will help with that.
If he is sitting in a recliner about 15 minutes before you get him up to go to the bathroom sit the chair up a bit. If he is on the couch or upright chair get him up and walk him a bit before going to the bathroom. Just this slight change might help.
Do discuss all of this with the doctor to rule out anything that may help with the situation.
This is easily, by the way, researched online with your favorite search engine. Just type in "incontinence and dementia" on the search bar.
I wish you the best.