Below is the LTspice simulation of a circuit that does what you want.
It uses CD4013 flip-flops (2 per package) as suggested by
rjenkinsgb.
Cross coupling each input to the opposite FF clear input provides both the alternation action desired, plus allowing both to be off by a second push of the same push=button.
Note that the push-buttons are momentary switches.
V1 and V4 simulate the PB operation.
The resistor and capacitor connected to the D inputs, provide the required debounce function for the mechanical push-buttons.
They prevent the FF from toggling again until after the debounce (RC) time.
I used P-MOSFETS to switch power to the circuits.
They can be just about any that can provide the required circuit current.
**broken link removed**