I think the problem is not in the relay coil because the circuit works well without the neon.
The the problem will be in the load.

You must be carefully in the use of static swich and inductive loads.
Is very comon than a triac dont opens when you want, because the daly between the V and I, and you must to design an RC for restoring the cos(phi). And after this if youy change the load for other inductive one you must to re design the RC for this new load.

Personaly i think is better to use a relay and good protections like a VDR, or RC (in this case is less critical) and a good supply.