I was very hesitant to get a minivan, and honestly still am not in love it with it, but with three kids (and often friends) it really is practical. Plus it's low enough to the ground that even the 2-year can climb in herself. My biggest complaint, though, is that it's terrible on ice and snow, so for 4WD is important to you, it sounds like a minivan won't be the best fit.
However, if you are in the market for a new car, I would definitely still consider a vehicle with 3 rows of seats. Yes, some (even most) cars will allow you to get three seat across, but it will be very squishy and if you drive more than very short distances I think you'll find the closeness will result in more arguing and such. Plus, kids grow so quickly, so the crowding problem will be ongoing, even after some of them are out of the carseats and boosters. I wouldn't necessarily go buy a new car just to have the third row, but if you're shopping anyway, I personally recommend it.
Also, when you go for test drives, take your carseats/boosters with you. It's sort of a pain, but it's nice to really try putting them in and seeing what the reality will be like. You might be able to fit them, but you're putting the kids in and out frequently, you may find you don't like having to squeeze your hand way down between seats to get everyone buckled, as it will make it more difficult for the kids to buckle themselves in as they get older. And then there's the kid who always seems to unbuckle the belt holding the baby's carseat in instead of the seat for their booster.
Good luck with your decision!