I'm rather confused as to the OP's situation. Why does it matter what network you're on for texting? There is no free mobile to mobile texting on any network. Texting AT&T to Verizon is the same for Verizon to Verizon. It's free mobile to mobile TALKING!
There are two scenario's here for your teens friends:
1. They're on Verizon and HAVE unlimited texting: great they have unlimited texting.....to both AT&T and Verizon.
2. They're on Verizon and they DON'T have unlimited texting (highly unlikely): they pay per message, same cost whether its from Verizon to Verizon or AT&T to Verizon.
Point: Texting is not like Voice. There is no free mobile to mobile within the network. You must pay for unlimited texting either way, or else pay per message, no matter where it originates from.
Your teens won't suffer from being on AT&T. In fact, its cheaper for family unlimited, and you get an iPhone!
All excellent points, and this is what I am discovering. Unlimited texting (from any network to any other network) is an added monthly cost. The difference in monthly charges between the two networks is negligible. So upon further research the points are all becoming moot. Most parents nowadays are foolish if they don't spring the extra bucks for unlimited texting for their teens.
It is looking like a family plan with AT&T, with one iPhone for me, will be no more than $30 per month more than the same number of regular phones on either carrier.
Now, the wild card is, how is AT&T service at my wife's parents house? Verizon is thin at best. If AT&T is significantly worse, or even non-existent, that could make a bigger difference than cost.
I think I will ask a friend with an iPhone to take a ride over and see how many bars he gets.