Pumps are rated at a delivery with zero head. To get a delivery at an increased head you need to look at the manufacturers charts. 2 bar is 30 metres head and I think it unlikely any 12V pump will deliver that.
To give you an example we have a 750W mains vortex pump (handles solids to 30mm diameter) rated at 4.5 litres per second, so a gallon, but at 9 metres head it reaches its limit and delivers nothing.
As Mab says, look at an alternative system.