If you have well water, you almost certainly have a pressure tank. The well pump runs until the pressure in the tank (and the overall system) is up to a predesignated level, then shuts off. The tank pressure then pushes water through the system until the pressure drops to a lower predetermined level. Then the pump motor kicks in again. This is supposed to maintain a relatively even pressure at the faucets.
If your pressure tank is not functioning (there is an air valve and an internal separator between water and the air in the tank and the water, either of which can cease to work correctly) this can interfere with maintaining satisfactory pressure and can cause the pump motor to run too frequently. There is also a pressure guage/valve/relay setup, usually a short pipe stem off the main water line near the pressure tank. If that pipe or valve get clogegd or optherwise stop working properly, the relay doesn't trip at the right time and the pressure can drop very low (even to zero) before pump kicks in again, raising the pressure.
You need someone to determine whether it is the tank or the pressure guage setup that is not functioning and act accordingly. Tanks are several hundreds of dollars, but a pressure valve fix is much less.
That sounds like an overly complicated setup with far more pumps than it should need. Or else you said pump when you meant tank in two places, actually, re-reading it.
In short, you can have as many pressure tanks as you like. Locating them closer to the point of use (the house) would be helpful, to a limited extent. That limited extent is the "effective volume" of the pressure tank at the house - while it's got pressure, you get better pressure at the house. As soon as it runs out of water and you become dependent on the pump, the pressure loss of the 300 feet of 1" PVC to the house comes into play, until you slow down your water use to the point where the pressure tank at the house fills up again.
If you do not change the setpoint pressure, the peak water pressure in the house will not be affected at all. Once the pressure tank at the house is depleted, the pressure will be the same as it is now. If you have a pressure gauge at the house now (or can add one) it might be useful to know the pressure at the house when "loads of interest" (showers, say) are drawing water.
Most pump controls can be altered to have a higher setpoint pressure, and most well pumps will provide that, within reason. General recommendations are to stay below 80 PSI - but if you are now running your pump on at 20 off at 40 (a typical default) you could turn it up to on at 30 off at 50, or on at 40 off at 60 - you will need to adjust your pressure tank (and any you may choose to add) for the higher pressure, particularly if they are bladder-type tanks - with the system drained, a bladder tank should typically be 2 PSI less than the low water pressure setpoint (ie, 18, 28, or 38 for the three ranges I've just given) and you may need additional pressure tank volume (because the effective volume of water a pressure tank can hold goes down as the system pressure goes up.) So, you can probably get more pressure without another pump, and possibly without another tank, but we'd need more details of what your system is doing now to know that for certain.
Unless your water use is extreme, 300 feet of 1" PVC pipe should not have a lot of effect on the pressure - at 5 gallons per minute, about 2.2 PSI - at 10GPM, 8.2PSI, 15 GPM, 17.4 psi
Best Answer
If the problem is undersized pipe, you need larger pipe, or some other coping mechanism such as a large pressure tank at the house.
Placing a pump on the end of the small pipe will likely cause the second pump to cavitate, which generally damages the pump. Water can only be sucked so hard before it boils, at any temperature.
If you want a pump on the house side, you can do that, but you'd need to provide a large cistern to serve as the water source for that pump, so it's drawing from the stored water in the cistern, not the too-small pipe.
A larger pipe is a much simpler solution to this problem in most cases.