Too funny, your situation is exactly the same as mine, right down to your MH size and the wife never learning to ride a bike.
As for a rack, Hollywood( I believe is the company) sells a rack that clamps around the spare. I have that, and it works very well for hauling bikes. As for the trike, I have not done it yet but I believe a platform carrier for the rear hitch would work. May have to spend a bit to get one long enough though.
As for getting the wife, a trike, like workman, folding trike or the trek plush I would advise against it. We started with a used Trek plus. The negatives were, pretty darn unstable, high center of gravity, hard to turn, very loosy goosy on any slanted or uneven pavement. She was not a fan.
Bought a Terra Rambler tadpole trike about a year ago. Have put many miles on it. Very stable, very fun to ride, light weight( about 40lbs). Stops well, disc brakes, 8 speed internal hub, fenders mirror, bag etc. Highly recommend a Tadpole trike for your wife.
They are not cheap. but for the enjoyment we have gotten out of it, and the physical exercise, I consider it money very well spent.
Will never forget the grin on my wife's face first time she rode one, went from skeptic to believer and I want this in about 15 seconds. My 2 cents for what it is worth
As an after thought they do make folding tadpoles. that also could be an option. But again not cheap.