Here's the schematic.
Inlined for convenience.
Nothing spectacularly wrong, there, though I do miss capacitors around the regulator. That may be the problem: the power dip when you switch on the relay may cause the ESP to misbehave. The capacitors are there to dampen those spikes.
A few minor issues:
GPIO2 connected to Vcc: not needed, the internal pull-up is enabled upon startup. Also it's much safer to add resistors here (like 10k) so you don't kill the port if you set it to output, low.
Likewise for GPIO15: this needs the pull-down, but better add a resistor, again for protection (in case you set it to output, high), and then you can also actually use this pin. It goes great as output for a MOSFET driver, as this normally also needs a pull-down.