Here is some literatire on some pressure tanks:
http://www.watertanks.com/images/pdf...s-hydropro.pdf
I'm throwing it there because you had mentioned volume of water. The pressure tank creates pressure for the system in such a way that for small draws the pump doesn't have to come on.
Yes, the pressure tank will affect the entire system. There really should not be a definite in or out. Air is compressable and the standard tank is a bladder tank, thus adding water compresses the bladder and at the high shuf off the pump shuts off. You can draw down the tank and at the low pressure setpoint the pump turns on, so you can get a glass of water or flush the toilet without the pump running. So, that's the basic purpose.
FLOW which you apparently want to increase will be dependent on the minimum size of pipe in the system UNLESS the storage resovour has a larger pipe size. That increased flow will only last for the amount that can be drawn down and then it's limited by the size of the line feeding the tank and the pump flow rate.
If you really need the FLOW and VOLUME what you might be able to do is burry a pressure tank in the barn with the right capacity for what you might consider an good draw down level.
So, if you determine that you would like about 40 gal at a high flow, then get another pressure tank in the system, but just have one controller for the pump.
It is possible to complicate matters, by sensing the pressures at both ends and make the pump turn on if either pressures drop. I doubt that would be necessary because in a static case the pressures will be the same throughout the system.
What I'm trying to say in a simple fashion is that if there is a 3/4" restriction somewhere and after that 3/4" restricting the pipe pize goes to 10" diameter, you canonly have the flow of a 3/4" pipe.
Initial low can only come from the size of the outlet of the and the draw down, so you would be able to maintain a high flow rate (Limited by the pipe diameter) until the draw down was exhausted.
After that happens, your limited by the smallest pipe size and the pump flow rate.
By putting a buried pressure tank near the barn, you can get that higher flow limited by the outlet size of the pressure tank for whatever time is desired. So if you need 40 gal to fill water troughs, washing, etc. for a short time get a tank to cover that.
Increasing a 3/4" outlet of a pump to 1.5" doesn't do a thing except decrease the friction loss of the pipe.
Burrying the pressure tank reduces the possibility of freezing.
This is somethingto consider because of the distances involved. Branch at the pump and go in two directions or branch at the house and go to the barn.
Friction loss will result in a pressure drop and a flow rate drop.
This is just an alternate thought.
Determine the flows required and the amount of water on an intermittant and continuous basis at the barn first.
The pipe lengths are very long.
FWIW: Sprinkler lines are buried all the time.