relay switching troubles
The problem its caused by the fact that \$Q_{18}\$ is always ON since  even when the input level fro Arduino Nano+ is high, it does not reach the 12V needed to bring \$V_{BE_{Q_{18}}}\simeq 0\$. This is due to the fact that the Arduino output reach at most +5V, while the emitter of \$Q_{18}\$ is connected with various loads (the relay coil and the series of the red LED and \$1\mathrm{k}\Omega\$ resistor. Therefore if you want your circuit to work correctly you have two possible choices:


Use two 5V coil relay and remove the 12V connect of the coils by connecting them to the 5V power supply as the two LEDs LD1 and LD2. This implies no circuit changes.
If you cannot use 5V relays since your supply current is limited, you can use two NPN transistors connected as shown below








simulate this circuit &ndash; Schematic created using CircuitLab

This circuit can work perfectly with the 5V/12V supply arrangement, at the cost of changing the \$Q_{18}\$ transistor.