Relay control to start and run my car

The 1N4001 suppression diodes have a peak inverse voltage of only 50 volts, which is a little low for your application. You might well expect 100+ volts being generated by a 12 volt relay coil when it releases. If you don't believe me try putting your fingers across the coil and then de-energising it !

It may be that the diodes have broken down and are passing current to the transistor when the relay is energised. In other words the transistor is having to pass a lot more current than just the coil current.

I'd suggest you go for higher rated diodes, such as 1N4003 or 1N4004, they don't cost any more and certainly won't break down at the voltages expected

One thing you should do is check the transistor current when the relays are energised to determine if they are passing more than expected.

jack