How about a used Lexus GX 470. I guess you'd probably have to go back to 2008-2009 to hit your price range and it won't get the gas mileage you want, but it should be reliable. I think there were problems with the rear shocks, but people often replaced the expensive air adjustable ones with ones from a 4runner without the expensive air lift.
8.3" of ground clearance and plenty of power. Should be capable going offroad. My brother has 4 kids and got a GX 470. At the time, he only had 3 though. Oldest was probably around 4yo, a 2yo and a newborn. He now has a honda oddysey and says the minivan is so much more convenient. He lives in suburban southern california though and has no need for offroad capabilities.
8.3" of ground clearance and plenty of power. Should be capable going offroad. My brother has 4 kids and got a GX 470. At the time, he only had 3 though. Oldest was probably around 4yo, a 2yo and a newborn. He now has a honda oddysey and says the minivan is so much more convenient. He lives in suburban southern california though and has no need for offroad capabilities.