Mutually exclusive latching momentary pushbuttons
The alternate-action function is not a part of a standard radio button circuit.
If there are only two active buttons, then this can be done with a dual D flipflop, such as a CD4013.  Each half is connected as a toggle ff, and each section's Q output is differentiated into the other section's Reset input.
EDIT:  First pass at a schematic.  R1-C1 debounces the switch input while keeping a fast signal edge at the clock input.  R2-C2 differentiates the Q output, and pulses the other circuit's Reset input when the Q output goes high.  You can adjust the component values for your switch behavior, inventory, etc.
Credit to Crutschow at AAC for the switch debounce trick.

Expanded explanation:
As you noted in your question, you need one toggle flipflop for each switch, plus something to manage the resetting of the other circuits.  The circuit I posted is pretty simple, but that is partly because it works for only two switches.  Expanding this circuit for more switches gets messy very quickly.
Connecting the inverting output of a D flipflop back to its D input creates a toggle flipflop, and a 4013 has two of them, so that is the basis for the circuit.  Without any of the cross-connection between the two circuits, you have two basic toggle circuits.
Switches bounce; that is, switch contacts do not come together cleanly.  They bounce off of each other and then come together again under the spring force.  When you press the button, the clock input can see dozens of signal edges in a few milliseconds.  Without treatment, this is a good random number generator.  R1-C1 is a lowpass filter that prevents the D input from changing as fast as the clock input is bouncing.  The first positive edge clocks the current Q- value into the ff.  this causes Q- to change to the other state, but the D input does not track this for about 16 milliseconds, approx 0.7 x the R-C time constant.  If the switch contacts still are bouncing after that time you will get sporadic circuit action; increase R1 or C1 to get a longer debounce period.
On ever other switch press, the Q output will go high.  C2-R2 form a highpass filter that functions as a differentiator.  When Q jumps from 0 v to Vcc (-ish), that high level appears immediately at pin 10, the Reset input of the other circuit, resetting U1B immediately.  Q will stay high until the next button press, and so will the end of C2 connected directly to it.  But R2 starts to charge up C2 by pulling the other end down to GND.  After (0.7 x R2 x C2) seconds, the voltage at pin 10 drops below the input transition level, releasing the Reset input so the circuit can accept inputs from SW2.  The reset pulse width is approx. 1.6 ms.
Note:  Missing from the sch is a decoupling capacitor for the chip.  Use another 0.22 uF cap connected directly to pins 7 and 14.