The clocks are part of a process I can't disclose, and which doesn't have any bearing on this specific problem.
Bzzzzt! You don't know how to do what you want; you've admitted that. But you're quite sure that explaining the purpose of your design "doesn't have any bearing" on solving your problem? I'm sure it would at least help me to understand what you're trying to do, and exactly what you need, since you are not clear on this yourself.
You don't need to worry that you're inventing the next Big Thing and someone here will steal your idea and patent it if you disclose it. I actually think it's quite rude to ask for help but deliberately withhold information that might help us help you.
If you were able to clearly define your requirements, it wouldn't be such an issue. But I think I've figured out what you want now.
When the slow clock goes high, the switch must pass the first analog input, no matter what the fast clock is doing (t so happens that the fast clock will always go high when the slow clock goes high, as you now know). But as soon as the fast clock goes high again, it switches the SPDT over to the 2nd analog input. The switch simply needs to remain in that position-- until the slow clock goes high again. So the intervening fast clock pulses could be safely ignored, if that would make things any easier.
OK. So on the rising edge of the slow clock, the output is forced low (say), even if there is a rising edge on the slow clock at the same time. Otherwise, rising edges on the fast clock set the output high.
This can be done easily with a D flip-flop (half a 4013). Tie the D input high, and feed the fast clock into the clock input. This takes care of the second part of your requirement. Then you need to convert rising edges on the slow clock into a short pulse that you can feed to the R input, to hold the flip-flop cleared (so it will ignore the clock pulse) during, and for a short time after, the rising edge on the slow clock. You can use a C-R differentiator for this:
. . . . . . . . . . . . . . . 1k . . 100 pF
Slow clock >----------\/\/\/\/-----| |------------------------> Reset input of flip-flop
. . . . . . . . . . . . . . . . . . . . . . . . .|
. . . . . . . . . . . . . . . . . . . . . . . . . ----\/\/\/\/-----0V
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10k
Tie the Set input low.