One single button to wake up a WeMos D1 and put it to sleep
At the very least, you're missing some parts.  A transistor inverter needs a pull-up resistor on the collector (or a pull-down if it's a PNP), at the very least you're missing those.  And it's difficult to do this sort of job with transistors in a way that is truly low power.
The way I'd do this is with an OR gate.  If you can deal with surface-mount parts, use a 1-gate chip, otherwise use the lowest-power 74xx32 that fits your voltage level (74HC32 if 5V).

The &quot;RESET&quot; signal goes to your WeMos's reset line.
The &quot;keep_on&quot; line comes from your WeMos - I'm assuming that the WeMos chip will let this pin float when it's in reset.  If it has an internal pull-up when it's reset, say so and we'll change the circuit.  You'll need to configure this as an output, and set it to high, when you power on, and accept that you'll use some current in the resistor when its on.
The &quot;button_pressed&quot; line goes back to some input on the WeMos.  Again, I'm assuming that the WeMos will let this line float when in reset.  If there's an internal pulldown in reset, then that'll cause problems.




simulate this circuit &ndash; Schematic created using CircuitLab