Peak current limiting motor
The TC4422 is a MOSFET gate driver and is not really intended to drive motors. 

The internal resistance is 6.3 ohms typically (could be 50% more when hot), so your current is being limited by the driver to not more than a couple amperes. You'll note that 18V/6.3 ohms is about 3A, so that's about the current you can momentarily get from it with maximum supply voltage into a short circuit (instantaneous power dissipation is 50W!). Actual current will be less because MOSFETs limit when the voltage drop gets high. Normally current flows to ground so only one switch is involved at a time.



I strongly suggest you get something beefier if you want to drive a relatively large motor like that. 

The 3A mentioned in the large print on the datasheet is for momentary currents drawn when charging and discharging the gate of a MOSFET, it is not a continuous current rating. Note also that the resistance measurement is made at low current (10mA), which prevents significant heating (so the numbers look good) and also at the highest power supply voltage (again which makes the numbers look better than you'll see at lower supply voltages). 

General rule with data sheets: The big print giveth and the small print taketh away. 

Do the measurements that Brian Drummond suggested to determine your actual requirements. The driver should be able to withstand the starting current without failing, either indefinitely (stalled motor) or with some kind of protection should that situation occur.