Is this the correct design to control the motor?

is this a right layout for controlling the motor ? and i want to use input 1 and 2 to trigger the on/off and forward/reverse. can it be done? thanks in advance for help.

You did good, however, I would put the NOT ENABLE relay close to the motor. The reason is, you can configure that relay to act as a dynamic brake which will prevent over-runs. And likely since the ports of a micro controller are configured as inputs, the motor doesn't move when initially powered up.

Just set that relay to short out the motor when off. For hobby motors, this works well.

There are "H-bridge" IC's which can interface to a motor. Direction and Not Enable is common, Some have "Coast" and "Brake" as well.