The only thing the MOSFET driver does is connect the MOSFET gate to VCC or GND via internal transistors.
This means any impedance in the driver's VCC or GND traces is then in series with the gate.
A decoupling capacitor next to the driver ensures a low power supply impedance for quick current delivery to the FET gate and fast switching. Without the capacitor, VCC will sag, potentially triggering undervoltage protection on the driver (if it has one) or not turning the FET on completely until VCC stabilizes.
However, inductance in series with the gate has another effect: it can make your FETs oscillate. If this occurs in a high current circuit they will usually explode.
The lack of decoupling caps in your design makes me thing you've never heard of this, so you should pay careful attention to the layout and routing of your gate traces, they should be short and low inductance. Add a low value resistor like 33R in series with the gate of each FET to prevent oscillation too. If you don't need it, you can always put a 0R resistor. But if you need it and you don't have the footprint, then... oops.
Likewise the GROUND connection from the driver to the FETs should be low-inductance, ideally a ground plane.
Note you also need a flyback diode that can take the full motor current.