OK I will try to explain this as best I can in writing. On my living room system that is my primary System that has PS+ Anybody can play all of my games and go online with it using my PS+. Now if you were to walk down to my bedroom and try you can't, I can though. I can go online anywhere in the world with my PS+. Because My second system has the games I have purchased on it and the fact that I have PS+ I am aloud to play on any system I want. Once I log into PSN all my account info is accessed. The only way anybody can play on my secondary console is #1, Play under my name or #2, They own the game themselves.
SO hear we go. Yes You will be bale to play on all three systems providing you are the purchaser. You could download you games you could download you games on a million systems and be able to play them. The catch is everything is linked to your account. If the world was to loose internet the only system you would be able to use is your primary system, you would be locked out of all others. Because your son has access to a game can only mean 2 things. #1, He is the purchaser or #2, he is playing on the purchasers primary console.
It's sort of hard to get your head around with just 2 systems so I do understand the confusion with 3,LOL. I own 4 PS4's and I tried everything but there is no getting around it. If you have more then 2 systems you have to buy the game twice. My oldest son and I both have PS+ and that allows all 4 of us to play online BUT it has to be done a certain way. My oldest sons Primary PS4 is in my youngest sons room. Doing this allows my youngest son to play online and access to my oldest sons library of games. My youngest Sons primary PS4 is in the older sons room. This allows the older son access to my younger sons game library. Now I can go into my youngest sons room and play any of my oldest sons games because it is my oldest sons primary PS4 But I can't go into his room and play my oldest sons game. He of course can play them because even though he isn't on his primary console he does own the games and because his PS+ is linked to them he has access as soon as he signs onto PSN.I also can not play my youngest sons games in my youngest sons room as his primary system is in his brothers room. All of his games have lock symbols on them. Once I go into his brothers room I do have access to them because I am now on my youngest sons primaryPS4. Even though I have PS+ I still need to have bought the game before I can play it. If my youngest son goes into his brothers room to play on his primary console he can't go online because he doesn't have PS+.
My youngest son and my wife can only use 2 systems in the house because of the fact that they do not have PS+. They only have access to online play on the primary PS4's of mine and my oldest sons. So even if you did get your 3rd son PS+ it won't do him any good. If you have more then 2 systems you will need to have at least 2 PS+ subscriptions and you will need to buy the games twice. Hope that helps and sorry for the bad news. If you have anymore questions ask away.