Circuit looks okay, however, I don't understand the purpose of D1 (I would use reference designator LED1), why not just tie to V+ to show you have power on? Also, you could have less devices and more universal relay driver if you use a NPN transistor to pull your external relay coils to ground, as shown in this similar circuit:
https://electronicsarea.com/on-off-switch-circuit-using-555-timer/ . Don't forget to use D1 on relay coil, as shown (D2 on second relay coil). Also, there are plenty of DPDT relays available, you just need to look around.
This looks suspiciously like a 9 volt battery driving your circuit and will last 10 minutes on your circuit driving the relays. I would find a small wall wart power supply
that delivers the current that you need at 9 to 15 volts.
I would also add a power on toggle switch for your circuit,
otherwise the battery will run down completely after one use. Strike that, just because the battery is not a good supply and you need a way to power on and off your circuit (see wall wart above).
EDIT: I would label the power switch that I mentioned "POWER", or "PWR" if you have limited space, with reference designator "S1" and label your SW1 "RUN" with reference designator "PB1" and label SW2 "STOP" with reference designator "PB2". But that is my style...