Switch to power pump with relay
I'd probably uses a small micro but if you want a non-programmed result then you can charge up a capacitor when a switch is held. The rate that the cap charges is determined by C and a resistor. You can choose RC values that equate to the capacitor attaining a terminal voltage of (say) 6 volts after 3 seconds. 

Use a comparator to detect that the capacitor has charged to 6 volts and this event can trigger a 555 timer in monostable mode. The 555 can drive a power transistor that can turn your motor.

What you haven't considered in your question is what happens if the switch is held on for the duration of the ten seconds and thru to 13 seconds - does the motor reactivate? 

Also, what is unclear is when the switch retriggers the 3 second timer during the 10 second timer - does the 10 second motor timer reset and extend from that instant.

Use a micro is my advice then you will be able to re-jig things at will.