For 3 kids now? I really would recommend the 2011 Odyssey, but I understand the budget. Only reason I would recommend the new body style is the new seat configuration of the middle row (you can fit all of your children there with any car seat front or rear facing...the middle row is a full seat with latch & tether). It also has a legitimate 3rd row for adults or children of all ages. That's the only knock that the Pilot has...that 3rd row is kid only and your cargo space is gone when it's up. Otherwise, get any Odyssey you can afford...automatic sliding doors, easy to fold seats, ease of getting in the 3rd row...all things as a new parent with an infant do NOT want to deal with that the other children can do on their own...safely (a lot tougher in an SUV with the higher ground clearance and smaller door openings).
The Armada/QX, Suburban/Escalade XLs, Excursions, and even Sequoias are all just too huge and way outside your budget for purchase and maintenance. They all have a legitimate 3rd row, albeit difficult for adults to get in and out of, and have enough cargo space even when the 3rd row is up. The new ones fold flat...IIRC the 3rd rows don't lay completely flat when down on those models.
I would definitely drive that Ford Flex...it's a little different than what you are probably used to. It has massive blind spots, rides lower, and is a little loud in the back if you have passengers back there trying to hear you talk up front (not to mention the 3rd row is child only). I love the look of it and the well equipped models are quite impressive. So like you, I like the look of it just didn't like the drive.