A very classic problem of which much has been written about.

It is pretty obvious that the motor is giving a big inductive kick when the relay opens. A VDR suitably rated would help here as previously suggested or more likely a snubber which consists of a resistor and capacitor in series. What values are they?? Depends on the motor - you might be trying to switch a 100kw motor for all we know. When I was younger (here we go....) we didn't know about the internet so one had to do a little leg work to solve one's problems. Equipment all around us switches motors on and off with microprocessors every day reliably - check out the electronics in a later model washing machine - you'll find answers there. Nothing like learning from someone more experienced and having an example to boot.

First rule of engineering : qualify and quantify. If you can't do this, we're talking black magic.

Let me tell you about the war.......