For all of you that need two SPI ports, two SPI ports are already embedded in the "regular" ATMega328p. That is if you don't need the USART. The USART can be configured to operate in MSPIM (Master SPI Mode). By the name of it you can conclude that the device only operates as master. But I guess that is fine for 99% of all MySensors applications?

Here is an Atmel application note concerning this matter:
http://www.atmel.com/Images/doc2577.pdf

Using an H-bridge can indicate that you want to reverse your engine. I guess that's not the case with the water pump?
The easy (quick and dirty) solution is to use a FET like in the "LED dimmer". But you should probably add a fly-back diode because of the inductive load.
Proposed solution depends on how robust you want it to be.

I think you should start by measuring voltage across VCC and GND on your Arduino pins when USB is not connected. On a lot of these breadboards "GND" and "VCC" rails are not connected the whole "width". Its not unusual that VCC is separated into two rails. Sometimes both VCC and GND are separated in the center of the rails.

Of course I can't see your actual setup but if it looks something like that image it can be a good idea to check connections between DC-plug and VCC/GND on you Arduino.

Worth a try.