Well, Tinovac, a lot of folks on this forum have tried to help and it doesn't seem we have gotten very far.
Reading back through this thread, I note that several people have mentioned the hitch latch, which, if not open, would cause exactly the complaints you have about ball size. But you have never mentioned that you have tried to open the latch, or given any indication that you know what we are talking about. I'm assuming now that you just don't have any past experience with towing or towing equipment.
In contrast, most of us just assume you know a little about hitches. Some of us probably learned at about 6 years old in 2 minutes watching our dads hook up a trailer, who answered any questions we had. So we just assume everybody knows some basics.
There has to be a latch to keep the trailer hitch from bouncing off the ball when driving around. There are a number of different latch designs and configurations I can think of right off the top of my head, at least 5 types I have owned personally. They don't all look even very similar. On my Hi-Lo, the latch control is a small rectangular metal box on top of the hitch just behind the ball socket. Yours could be different.
The control handle or lever or whatever they used is connected to a plate under the hitch that, once fastened, prevents the ball from slipping out of the socket. Also, if the latch is closed when you try to insert the ball, there's no way you can get it in. That would explain why you can't get a 2 5/16" ball into the socket, and why the smaller 2" would rattle around in it. (Your tow guy who brought the trailer to your place wasn't hooked up safely if a 2" ball was loose in the hitch, which could have come off when going over a bump. Unless he had some other tie-down for the purpose.)
If I am correct about the source of your problem, I note that several folks on here have suggested you get someone competent about towing to show you some things in person. We can't offer a good substitute for that. Don't just order things off the Internet or buy at a Walmart if you don't know what you are doing. If an item costs a little more at an RV dealer, his expertise is well worth paying a bit for. You can be frugal later when you get some experience.
I hope this is helpful. If I'm all off-base here, sorry.
