It would seem to me that there are a number of issues here, and consequently a similar range of solutions.

Option 1. Flicking wife - not for the faint hearted, nor the financially challenged.

Option 2. Flicking the cats - see (1.) above - the two are probably inextrickably inter-related.

Option 3. Flicking both - kill yourself (slowly, and incredibly painfully - video it for best effect) - it's cheaper and easier.

Option 4. the 'classical conditioning option'. Every time said cat(s) approach the rug, yell you're heart out and throw something at them, for example, a 130g, 277 cal projectile. Now, 'throwing' is defined entirely by the user, and in so doing, absolves and indemnifies all other persons, living or deceased from any responsibility as the humaneness, efficacy, or logic (especially in the lounge room) of the outcome of their practices and / or beliefs...

I'm with Big Sky! Get rid of both the cats & the wife!!! But seriously, I think everbody ought to have 2 cats in their house! I do! One on each side of the fireplace.

Regards Mike

How about a couple of cat-skin rugs right next to the bear skin?

How 'bout 36 grains of lead, applied to the forehead of each cat?