I went with a MAX with the captains chairs, drove a short one, it's still the same width/huge/etc. Turning radius is wicked on either coming from an Access Cab Tacoma. We didn't consider getting anything smaller w/4 kids. It holds plenty and pulls the shit out of the TT.
That being said, I put my wife, her mother, my 4 kids and my 2 nieces in our 2013 Odyssey this AM w/luggage, 2 coolers, 2 car seats, 1 booster, and a jogging stroller. It fits more people/crap than the MAX and preserves the rear view mirror sight-line. If I had a 8 passenger, the MAX would've needed a roof top carrier for a 3 night trip for that crew if you want to see what is in the rear view mirror - I'll concede it doesn't matter much in some cases, but, I still prefer seeing behind me in all the mirrors.
3 kids would fit comfortably across the 2nd row (carseats/booster/etc.) of a regular one and you'd have a huge amount of space with the 3rd row down. Just a pain in the ass getting them in and out as well as the door dings from some wind or kids being kids getting in and out in close quarters.
If you end up with 3+ kids/routinely use it for people moving/travel and don't opt for a sliding door minivan, it's your ego not going with the common sense solution there. I could've bought almost 3 brand new minivans for the price of this beast! At the end of the day, it is preference. YMMV.
Good luck/happy shopping!