I hate to say this but I think the general premise that it be a 180 or a Cub is flawed, although both are outstanding aircraft (or so I've been told by others).
Lets talk about safety first. We all know a plane with its third wheel at the back is much harder to fly then those with the tiny wheel up front. Okay never mind about the safety first thing, let's move on.
Lets talk about construction. Your Dad would probably appreciate a plane made from concrete, but unfortunately none of those are still flying, which might explain what happened to Jimmy Hoffa. So that brings us to Steel or Aluminium?
Common sense tells us that steel is much stronger then Aluminium, although everytime I walk into a wing strut on one of those stupid high wing planes it leaves a knot on my forehead, so Aluminium is apparently some pretty strong stuff. Which reminds me, lets talk about wing location. And I don't mean those crazy airplanes with the tail up front and the wing in the back. Reminds of the time when I turned a Taildragger into a trike when I got a deal on a Russian propellor - but that's another story.
Where was I? Oh yea, wings. We all know the propensity of taildraggers to ground loop. Under such a circumstance there is a distinct advantage to low wing airplanes. In almost no time at all the wing is gently carasseing the ground thereby providing stability as the airplane rotates around the yaw axis. Note: you might want your Dad to read this as I am introducing important aeronautical terms while at the same time discussing flying techniques such as "slips across the ground" and whether a whiskey compass leads a heading change or follows it in a ground loop to the left or right. And if we think about the "float" that Mooneys and Saratogas have, we can see that a low wing is far superior in a Taildragger trainer. At this point one might think a RV would fit the bill, but alas, there are no STCs yet for 26" or larger tires.
Continuing on the wing theme there can be made a case for the high wing.
1. On the ground they provide an abundance of shade, and help keep us dry during passing rain showers.
2. In the air they keep the sun out of he cockpit (with a few exceptions) thus reducing the greenhouse effect, unless of course you happen to be flying with Al Gore.
So as we can see a case can be made for both high and low wing airplanes, seemingly complicating your decision, but not really. You are not the first person who has faced this decision. In point of fact both the US Navy and the US Army had this decision to make even before World War II. There choice was unanimous. They chose both the high and the low wing. They chose the Boeing Stearman.
Hang on, bear with me here, let's look at what makes the Stearman the ultimate Taildragger backcountry trainer:
1. Over 70 years of keeping its students safe in the enevitable "incidents".
2. Your Dad will learn about the poor visibility traits of both the high wing and low wing airplanes AT THE SAME TIME reducing the amount of "dual" needed.
3. Tire/wheels are 27" tall, an excellent compromise between 26s and 29s, without becoming ostentatious like those guys with the 31s and 35s, I mean really, are we still in high school?
4. 220 horsepower engine is stock so your Dad gets a high performance checkout as part of his private.
5. Planes gross is over 3,000 pounds so the horsepower is "not quite enough" to get him in trouble.
6. Planes net is over 2,000 pounds so will encourage your Dad to eat healthy and not be suckered in to that Lemonaide diet (which I'm pretty sure was made up by kids with Lemonaide stands - you can find anything on the Internet today)
7. Only holds about 40 gallons useable and burns about 18gph which is great when you become my and your Dads age. "No, I don't have a bladder problem, I need to stop for fuel". Its all about perception as you'll find out.
8. Leaks oil so your Dad won't have to worry about looking under the engine area to see if there's a leak - there is. Also he won't have to worry about his knees or back getting under the belly to clean it - what's the point. In fact, the only thing he needs to concern himself about oil is if the leak stops - means it's out of oil.
9. Your Dad can land anywhere he wants and never never never piss anyone off. "Wow that is such a cool plane! Please come back anytime you want".
I could go on and on (and I will).
Lets talk about your Mom for a minute. You've told me she loves to fly with you, hate to burst your bubble but all Moms say that even if they are terrified, but lets assume for discussions sake that you are right. At first you might think a Stearman, with only two seats and a baggage compartment, might preent a problem for your Dads mission of taking your Mom, two dogs and an ice chest - but I don't believe it will be. I know your Mom supports your Dad completely, and has "indicated" she enjoys flying with you. Well I say get her involved in aviation as well, but not as a pilot or co-pilot (boring) but as a Wing Walker! Then she will enjoy those flights out to the ranch with visibility unencumbered by wings or fuselage. Plus there is the added bonus that she could repair things like minor tears in the fabric IN FLIGHT, no need for those unneccesary landings. And when your Dad is flying along those rivers your Mom will be in a much better position to tell your Dad if they can make it under those power lines then he will.
So with your Mom on the wings that frees up the front cockpit and baggage compartment for the dogs. This will significantly improve their level of obedience and unconditional love towards your Dad as they will now both try to gain favor.
And if all this wasn't enough your Dad, learning in his Stearman, will be the coolest student ever, period. Cubs and Wagons (okay Maules too) have great ramp appeal to pilots, but lets face it they are just another airplane to the general public. Stearmans have outstanding ramp presence and appeal to everyone. Oh, and I just so happen to have one for sale.