You have a few things going on here. The pump kicking on without water use would indicate a bad check valve or a leak in the system.
With the pump and the pressure there could be many things. How is your well? Is it strong enough to pump water for the irrigation system? The irrigation system and the house? Do the sprinkler heads run consistently or do they surge as though the water level in the well has dropped below the pump?
If your well is strong enough, you low water pressure in the house indicates that along with drawing the well down, you are getting over to the left hand side of you pump curve where you are able to pump lots of water but little pressure. You could install a bigger pump in the well that would be designed to handle both the load of the irrigation system and that of the house. The downfall to this is that the pump will run very erratically under very small water usages. I would say that the pump would “hammer on and off” under small water usages. A good solution to this would be to install a constant pressure system or a variable speed pump drive. The company I work for has installed many of these on systems with problems like yours. Keep in mind that you need a high volume well to use one of these. These systems will maintain a constant pressure rather than a pressure range like a pressure switch. In addition, the pump will vary the speed and flow produced to maintain this pressure. This eliminates the “hammer on and hammer off” with a large pump on a pressure switch. Other advantages are improved motor protection and troubleshooting codes that can make service calls easier for the pump installer. I would recommend the Franklin Electric Monodrive or Subdrive as we have had really good luck with these. The Monodrive is better as its components are typically more stocked by most good pump installers. Also, almost any submersible pump out there will already be powered by a Franklin Electric motor. Goulds and Grundfos also make good systems. A constant pressure pump would be a better alternative than a booster pump.