the power for the arduino could be from the USB, but the USB will never deliver enough power for multiple relays.
you should have a separate power supply for the relays and a separate one for the Arduino.
tie the grounds together.
the contacts side of the relay are totally isolated and those connections should not be connected to either of the other power supplies.
in reality, if you are using the same power supply for the motor, you could just use a transistor and not the relays.
what you did not list
#1) the power consumption rating for the relays coils.
#2) the relay part number. a link to the data sheet would be welcome.
#3 ) the relay coil power supply ratings, how much current does it deliver
#4) the part number for the transistor.
#5) the math to show why you chose that resistor.
fundamentally, you do not have any problems.
however, the implementation sounds like it needs some attention.
I edited your drawing to show separations of power supplies.
relay.bmp (144 KB)
