you want to look at a bi-stable solenoid then.
EDIT: actually on reflection the circuit i drew up could work, give me a couple minutes 
EDIT 2:
Right here we go
So this circuit is based off my other circuit which gives you a toggling output from a valid scan output of the xAC.
However what you would do rather than conncting the remote buttons you would add the below circuit.
This circuit uses the 2 toggling outputs to dive 2 relays that will in turn toggle your solenoid.
Use this type of solenoid and this type of relay and you should be golden. Note parts linked are only as guidance and may not actually work but the important thing is the type of part. Also worth pointing out door lock solenoids are bi-stable so definitely go for them!
Full circuit for completeness.
