I've built I circuits in the past for driving relays, and sometimes the electric pulse generated by its activation affects its operation.Hmm. What neither my sim nor yours explicitly shows are the power connections to the IC. Do you have a decoupling cap (100nF) between pins 7 (GND) and pin 14 (V+), very close to the pins?
I've had to add strong decoupling caps (in the order of 4.7 uF and up) along with the standard 100 nF for the circuit to stabilize.