We plan on going on 12 mile rides on a paved but hilly trail
I think you should make it interesting for yourself: get a 16" uni and just ride the hell out of it to keep up. Then you deserve a medal for it.
But seriously, pushing beyond 10 km/h on a 16" is exhausting and scary! 
I dunno. The seat on my 16” is too small. Its for the kids anyways
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16" was my only uni for 2 years, and I’ve been able to ride on bumpy, hilly 2 mile rides. Back then I didn’t really think about wheel size at all
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A 29 with not-too-long cranks (say sub 125mm) can do that distance for sure and sounds great for that as long as you don’t expect to be keeping up with “normal” faster cyclists and the bike riders are ok with more of a leisurely pace.
Enjoy the ride with your family. Even if you aren’t always side by side together. You are getting outside and exercising, what a lot of people lack these days.
I did this with my wife and daughter a few times. Neither my wife nor daughter are fast riders on their bikes. Despite that they left me behind without even trying. It didn’t help that I’m a slower rider by default. A bigger wheel does help but you may still find yourself falling behind if your dad puts some effort in to getting speed. Enjoy the ride.