Howdy Doc
we are in similar situation - 6kids, 7th on the way. Adoption - Badass! congratulations and thanks for your efforts!
We also save 50%+, I cycle to work most days, DW is SAHM and part time fitness instructor. We too enjoy family road trip vacations. I'm also a gearhead/petrolhead and spent a lot of time on this topic.
2 major options:
1) Chevy 3500 van, 12 or 15 pass. Specifically, 2010 and up, 1 ton. They have the excellent 6.0 engine and 6spd tranny. Extremely reliable. 16-18mpg highway with a light foot. AC will freeze an Eskimo. plenty of power. Downside: ride like a 1 ton truck, which it is. This is what I have. i spent some time & a couple hundred bucks adding insulation, nice shocks, tint etc which improved it somewhat, but it is a crude implement.... The 1/2ton, and pre2010, have substanard trannies. GMC Savanna is the same van, much harder to find, a bit nicer.
2) Ford Transit 10-15pass. Upside: much more modern, quiet, refined. Downside: Spendier, and the base 3.7V6 is barely adequate. unknown reliability, though should be good.
Avoid older vans (reliability issues) and 'SUVs' - suburba, armada, etc. Small and expensive.
Good luck!!