Hi Tgreen! There is a forum dedicated to the camino and they have a section specifically for "alternative transport" to help you with the logistics of driving the actual route.
https://www.caminodesantiago.me/community/forums/alternative-transportation.37/
From what I understand, you can still get snow up in the mountains in April. So plan accordingly if you want to go all of the way into France.
With regards to the "Are we crazy?" We are all a little crazy! To me, it sounds like a lot of driving unless you are going to be in the area for a a couple of weeks at least. But, if road tripping is your thing, go for it. I am sure people more familiar with driving in the area will chime in.