Latching relay not working
Just to be sure we're on the same page, relay coils are between pins 1-12 and 6-7, not between 3-10. Also note that Q2 has some voltage drop even when turned on, so if you set the PSU to the latching voltage, the relay will see a smaller voltage and may not activate. Set the PSU to "rated" voltage, i.e. 5V. You could even leave it at 9V, since the relay is guaranteed to withstand up to 10.9V, though that's getting pretty close to the limit which is OK for a prototype but not advised for long-term usage.