Latching Relay Driver
I see you are still looking at these DC relays. Nice choice, actually. You can select either one coil, or two. The two-coil version would be a bit easier. The one-coil version will require what amounts to a kind of H-bridge (or in amplifier terms, bridge-tied load) configuration. So I get why you are struggling.

Let's start with the two-coil variety, as that is much easier:







simulate this circuit &ndash; Schematic created using CircuitLab

That's one way of handling it. Note that the BJTs can be small signal, it seems. But they should be rated for perhaps \$400\:\textrm{mA}\$ or better, just in case. This will require \$10\:\textrm{mA}\$ from your I/O pins.

If you want to use the one-coil variety, the circuit becomes a little more complex because you need both high side and low side driver BJTs and you need them for both I/O pins, so that's four transistors.

Let me know if you want a schematic for that.